diff --git a/graph/community/bisect_test.go b/graph/community/bisect_test.go
index 37e20370..12a75dbb 100644
--- a/graph/community/bisect_test.go
+++ b/graph/community/bisect_test.go
@@ -62,7 +62,7 @@ func init() {
 	friends = simple.NewWeightedUndirectedGraph(0, 0)
 	for u, e := range middleEast.friends {
 		// Ensure unconnected nodes are included.
-		if !friends.Has(simple.Node(u)) {
+		if !friends.Has(int64(u)) {
 			friends.AddNode(simple.Node(u))
 		}
 		for v := range e {
@@ -72,7 +72,7 @@ func init() {
 	enemies = simple.NewWeightedUndirectedGraph(0, 0)
 	for u, e := range middleEast.enemies {
 		// Ensure unconnected nodes are included.
-		if !enemies.Has(simple.Node(u)) {
+		if !enemies.Has(int64(u)) {
 			enemies.AddNode(simple.Node(u))
 		}
 		for v := range e {
@@ -127,7 +127,7 @@ func TestProfileUndirected(t *testing.T) {
 		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -144,7 +144,7 @@ func TestProfileWeightedUndirected(t *testing.T) {
 		g := simple.NewWeightedUndirectedGraph(0, 0)
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -186,7 +186,7 @@ func TestProfileDirected(t *testing.T) {
 		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -203,7 +203,7 @@ func TestProfileWeightedDirected(t *testing.T) {
 		g := simple.NewWeightedDirectedGraph(0, 0)
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
diff --git a/graph/community/k_communities_test.go b/graph/community/k_communities_test.go
index 9861b2d7..46a31e64 100644
--- a/graph/community/k_communities_test.go
+++ b/graph/community/k_communities_test.go
@@ -111,7 +111,7 @@ func TestKCliqueCommunities(t *testing.T) {
 		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
diff --git a/graph/community/louvain_common.go b/graph/community/louvain_common.go
index be68e094..f0ebce39 100644
--- a/graph/community/louvain_common.go
+++ b/graph/community/louvain_common.go
@@ -359,10 +359,10 @@ const (
 // positiveWeightFuncFor returns a constructed weight function for the
 // positively weighted g. Unweighted graphs have unit weight for existing
 // edges.
-func positiveWeightFuncFor(g graph.Graph) func(x, y graph.Node) float64 {
+func positiveWeightFuncFor(g graph.Graph) func(xid, yid int64) float64 {
 	if wg, ok := g.(graph.Weighted); ok {
-		return func(x, y graph.Node) float64 {
-			w, ok := wg.Weight(x, y)
+		return func(xid, yid int64) float64 {
+			w, ok := wg.Weight(xid, yid)
 			if !ok {
 				return 0
 			}
@@ -372,8 +372,8 @@ func positiveWeightFuncFor(g graph.Graph) func(x, y graph.Node) float64 {
 			return w
 		}
 	}
-	return func(x, y graph.Node) float64 {
-		e := g.Edge(x, y)
+	return func(xid, yid int64) float64 {
+		e := g.Edge(xid, yid)
 		if e == nil {
 			return 0
 		}
@@ -384,10 +384,10 @@ func positiveWeightFuncFor(g graph.Graph) func(x, y graph.Node) float64 {
 // negativeWeightFuncFor returns a constructed weight function for the
 // negatively weighted g. Unweighted graphs have unit weight for existing
 // edges.
-func negativeWeightFuncFor(g graph.Graph) func(x, y graph.Node) float64 {
+func negativeWeightFuncFor(g graph.Graph) func(xid, yid int64) float64 {
 	if wg, ok := g.(graph.Weighted); ok {
-		return func(x, y graph.Node) float64 {
-			w, ok := wg.Weight(x, y)
+		return func(xid, yid int64) float64 {
+			w, ok := wg.Weight(xid, yid)
 			if !ok {
 				return 0
 			}
@@ -397,8 +397,8 @@ func negativeWeightFuncFor(g graph.Graph) func(x, y graph.Node) float64 {
 			return -w
 		}
 	}
-	return func(x, y graph.Node) float64 {
-		e := g.Edge(x, y)
+	return func(xid, yid int64) float64 {
+		e := g.Edge(xid, yid)
 		if e == nil {
 			return 0
 		}
diff --git a/graph/community/louvain_directed.go b/graph/community/louvain_directed.go
index bb4ef6c9..ce26cb71 100644
--- a/graph/community/louvain_directed.go
+++ b/graph/community/louvain_directed.go
@@ -34,24 +34,28 @@ func qDirected(g graph.Directed, communities [][]graph.Node, resolution float64)
 	for _, n := range nodes {
 		var wOut float64
 		u := n
-		for _, v := range g.From(u) {
-			wOut += weight(u, v)
+		uid := u.ID()
+		for _, v := range g.From(uid) {
+			wOut += weight(uid, v.ID())
 		}
 		var wIn float64
 		v := n
-		for _, u := range g.To(v) {
-			wIn += weight(u, v)
+		vid := v.ID()
+		for _, u := range g.To(vid) {
+			wIn += weight(u.ID(), vid)
 		}
-		w := weight(n, n)
+		id := n.ID()
+		w := weight(id, id)
 		m += w + wOut // We only need to count edges once.
-		k[n.ID()] = directedWeights{out: w + wOut, in: w + wIn}
+		k[id] = directedWeights{out: w + wOut, in: w + wIn}
 	}
 
 	if communities == nil {
 		var q float64
 		for _, u := range nodes {
-			kU := k[u.ID()]
-			q += weight(u, u) - resolution*kU.out*kU.in/m
+			uid := u.ID()
+			kU := k[uid]
+			q += weight(uid, uid) - resolution*kU.out*kU.in/m
 		}
 		return q / m
 	}
@@ -59,10 +63,12 @@ func qDirected(g graph.Directed, communities [][]graph.Node, resolution float64)
 	var q float64
 	for _, c := range communities {
 		for _, u := range c {
-			kU := k[u.ID()]
+			uid := u.ID()
+			kU := k[uid]
 			for _, v := range c {
-				kV := k[v.ID()]
-				q += weight(u, v) - resolution*kU.out*kV.in/m
+				vid := v.ID()
+				kV := k[vid]
+				q += weight(uid, vid) - resolution*kU.out*kV.in/m
 			}
 		}
 	}
@@ -203,23 +209,27 @@ func reduceDirected(g graph.Directed, communities [][]graph.Node) *ReducedDirect
 
 			var out []int
 			u := n
-			for _, v := range g.From(u) {
-				vid := communityOf[v.ID()]
-				if vid != id {
-					out = append(out, vid)
+			uid := u.ID()
+			for _, v := range g.From(uid) {
+				vid := v.ID()
+				vcid := communityOf[vid]
+				if vcid != id {
+					out = append(out, vcid)
 				}
-				r.weights[[2]int{id, vid}] = weight(u, v)
+				r.weights[[2]int{id, vcid}] = weight(uid, vid)
 			}
 			r.edgesFrom[id] = out
 
 			var in []int
 			v := n
-			for _, u := range g.To(v) {
-				uid := communityOf[u.ID()]
-				if uid != id {
-					in = append(in, uid)
+			vid := v.ID()
+			for _, u := range g.To(vid) {
+				uid := u.ID()
+				ucid := communityOf[uid]
+				if ucid != id {
+					in = append(in, ucid)
 				}
-				r.weights[[2]int{uid, id}] = weight(u, v)
+				r.weights[[2]int{ucid, id}] = weight(uid, vid)
 			}
 			r.edgesTo[id] = in
 		}
@@ -270,43 +280,47 @@ func reduceDirected(g graph.Directed, communities [][]graph.Node) *ReducedDirect
 		var out, in []int
 		for _, n := range comm {
 			u := n
+			uid := u.ID()
 			for _, v := range comm {
-				r.nodes[id].weight += weight(u, v)
+				r.nodes[id].weight += weight(uid, v.ID())
 			}
 
-			for _, v := range g.From(u) {
-				vid := communityOf[v.ID()]
+			for _, v := range g.From(uid) {
+				vid := v.ID()
+				vcid := communityOf[vid]
 				found := false
 				for _, e := range out {
-					if e == vid {
+					if e == vcid {
 						found = true
 						break
 					}
 				}
-				if !found && vid != id {
-					out = append(out, vid)
+				if !found && vcid != id {
+					out = append(out, vcid)
 				}
 				// Add half weights because the other
 				// ends of edges are also counted.
-				r.weights[[2]int{id, vid}] += weight(u, v) / 2
+				r.weights[[2]int{id, vcid}] += weight(uid, vid) / 2
 			}
 
 			v := n
-			for _, u := range g.To(v) {
-				uid := communityOf[u.ID()]
+			vid := v.ID()
+			for _, u := range g.To(vid) {
+				uid := u.ID()
+				ucid := communityOf[uid]
 				found := false
 				for _, e := range in {
-					if e == uid {
+					if e == ucid {
 						found = true
 						break
 					}
 				}
-				if !found && uid != id {
-					in = append(in, uid)
+				if !found && ucid != id {
+					in = append(in, ucid)
 				}
 				// Add half weights because the other
 				// ends of edges are also counted.
-				r.weights[[2]int{uid, id}] += weight(u, v) / 2
+				r.weights[[2]int{ucid, id}] += weight(uid, vid) / 2
 			}
 		}
 		r.edgesFrom[id] = out
@@ -316,8 +330,7 @@ func reduceDirected(g graph.Directed, communities [][]graph.Node) *ReducedDirect
 }
 
 // Has returns whether the node exists within the graph.
-func (g *ReducedDirected) Has(n graph.Node) bool {
-	id := n.ID()
+func (g *ReducedDirected) Has(id int64) bool {
 	return 0 <= id && id < int64(len(g.nodes))
 }
 
@@ -331,8 +344,8 @@ func (g *ReducedDirected) Nodes() []graph.Node {
 }
 
 // From returns all nodes in g that can be reached directly from u.
-func (g *ReducedDirected) From(u graph.Node) []graph.Node {
-	out := g.edgesFrom[u.ID()]
+func (g *ReducedDirected) From(uid int64) []graph.Node {
+	out := g.edgesFrom[uid]
 	nodes := make([]graph.Node, len(out))
 	for i, vid := range out {
 		nodes[i] = g.nodes[vid]
@@ -341,8 +354,8 @@ func (g *ReducedDirected) From(u graph.Node) []graph.Node {
 }
 
 // To returns all nodes in g that can reach directly to v.
-func (g *ReducedDirected) To(v graph.Node) []graph.Node {
-	in := g.edgesTo[v.ID()]
+func (g *ReducedDirected) To(vid int64) []graph.Node {
+	in := g.edgesTo[vid]
 	nodes := make([]graph.Node, len(in))
 	for i, uid := range in {
 		nodes[i] = g.nodes[uid]
@@ -351,9 +364,7 @@ func (g *ReducedDirected) To(v graph.Node) []graph.Node {
 }
 
 // HasEdgeBetween returns whether an edge exists between nodes x and y.
-func (g *ReducedDirected) HasEdgeBetween(x, y graph.Node) bool {
-	xid := x.ID()
-	yid := y.ID()
+func (g *ReducedDirected) HasEdgeBetween(xid, yid int64) bool {
 	if xid == yid || !isValidID(xid) || !isValidID(yid) {
 		return false
 	}
@@ -366,9 +377,7 @@ func (g *ReducedDirected) HasEdgeBetween(x, y graph.Node) bool {
 }
 
 // HasEdgeFromTo returns whether an edge exists from node u to v.
-func (g *ReducedDirected) HasEdgeFromTo(u, v graph.Node) bool {
-	uid := u.ID()
-	vid := v.ID()
+func (g *ReducedDirected) HasEdgeFromTo(uid, vid int64) bool {
 	if uid == vid || !isValidID(uid) || !isValidID(vid) {
 		return false
 	}
@@ -378,15 +387,13 @@ func (g *ReducedDirected) HasEdgeFromTo(u, v graph.Node) bool {
 
 // Edge returns the edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g *ReducedDirected) Edge(u, v graph.Node) graph.Edge {
-	return g.WeightedEdge(u, v)
+func (g *ReducedDirected) Edge(uid, vid int64) graph.Edge {
+	return g.WeightedEdge(uid, vid)
 }
 
 // WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g *ReducedDirected) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
-	uid := u.ID()
-	vid := v.ID()
+func (g *ReducedDirected) WeightedEdge(uid, vid int64) graph.WeightedEdge {
 	if uid == vid || !isValidID(uid) || !isValidID(vid) {
 		return nil
 	}
@@ -401,9 +408,7 @@ func (g *ReducedDirected) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
 // If x and y are the same node the internal node weight is returned. If there is no joining
 // edge between the two nodes the weight value returned is zero. Weight returns true if an edge
 // exists between x and y or if x and y have the same ID, false otherwise.
-func (g *ReducedDirected) Weight(x, y graph.Node) (w float64, ok bool) {
-	xid := x.ID()
-	yid := y.ID()
+func (g *ReducedDirected) Weight(xid, yid int64) (w float64, ok bool) {
 	if !isValidID(xid) || !isValidID(yid) {
 		return 0, false
 	}
@@ -433,7 +438,7 @@ type directedLocalMover struct {
 	// that returns the Weight value
 	// of the non-nil edge between x
 	// and y.
-	weight func(x, y graph.Node) float64
+	weight func(xid, yid int64) float64
 
 	// communities is the current
 	// division of g.
@@ -484,18 +489,21 @@ func newDirectedLocalMover(g *ReducedDirected, communities [][]graph.Node, resol
 	for _, n := range l.nodes {
 		u := n
 		var wOut float64
-		for _, v := range g.From(u) {
-			wOut += l.weight(u, v)
+		uid := u.ID()
+		for _, v := range g.From(uid) {
+			wOut += l.weight(uid, v.ID())
 		}
 
 		v := n
 		var wIn float64
-		for _, u := range g.To(v) {
-			wIn += l.weight(u, v)
+		vid := v.ID()
+		for _, u := range g.To(vid) {
+			wIn += l.weight(u.ID(), vid)
 		}
 
-		w := l.weight(n, n)
-		l.edgeWeightsOf[n.ID()] = directedWeights{out: w + wOut, in: w + wIn}
+		id := n.ID()
+		w := l.weight(id, id)
+		l.edgeWeightsOf[id] = directedWeights{out: w + wOut, in: w + wIn}
 		l.m += w + wOut
 	}
 
@@ -562,7 +570,7 @@ func (l *directedLocalMover) move(dst int, src commIdx) {
 func (l *directedLocalMover) deltaQ(n graph.Node) (deltaQ float64, dst int, src commIdx) {
 	id := n.ID()
 
-	a_aa := l.weight(n, n)
+	a_aa := l.weight(id, id)
 	k_a := l.edgeWeightsOf[id]
 	m := l.m
 	gamma := l.resolution
@@ -613,8 +621,8 @@ func (l *directedLocalMover) deltaQ(n graph.Node) (deltaQ float64, dst int, src
 				removal = true
 			}
 
-			k_aC.in += l.weight(u, n)
-			k_aC.out += l.weight(n, u)
+			k_aC.in += l.weight(uid, id)
+			k_aC.out += l.weight(id, uid)
 			// sigma_totC could be kept for each community
 			// and updated for moves, changing the calculation
 			// of sigma_totC here from O(n_c) to O(1), but
diff --git a/graph/community/louvain_directed_multiplex.go b/graph/community/louvain_directed_multiplex.go
index 2f1a6060..a695b80a 100644
--- a/graph/community/louvain_directed_multiplex.go
+++ b/graph/community/louvain_directed_multiplex.go
@@ -63,7 +63,7 @@ func qDirectedMultiplex(g DirectedMultiplex, communities [][]graph.Node, weights
 			layerResolution = resolutions[l]
 		}
 
-		var weight func(x, y graph.Node) float64
+		var weight func(xid, yid int64) float64
 		if layerWeight < 0 {
 			weight = negativeWeightFuncFor(layer)
 		} else {
@@ -77,15 +77,18 @@ func qDirectedMultiplex(g DirectedMultiplex, communities [][]graph.Node, weights
 		for _, n := range nodes {
 			var wOut float64
 			u := n
-			for _, v := range layer.From(u) {
-				wOut += weight(u, v)
+			uid := u.ID()
+			for _, v := range layer.From(uid) {
+				wOut += weight(uid, v.ID())
 			}
 			var wIn float64
 			v := n
-			for _, u := range layer.To(v) {
-				wIn += weight(u, v)
+			vid := v.ID()
+			for _, u := range layer.To(vid) {
+				wIn += weight(u.ID(), vid)
 			}
-			w := weight(n, n)
+			id := n.ID()
+			w := weight(id, id)
 			m += w + wOut // We only need to count edges once.
 			k[n.ID()] = directedWeights{out: w + wOut, in: w + wIn}
 		}
@@ -93,8 +96,9 @@ func qDirectedMultiplex(g DirectedMultiplex, communities [][]graph.Node, weights
 		if communities == nil {
 			var qLayer float64
 			for _, u := range nodes {
-				kU := k[u.ID()]
-				qLayer += weight(u, u) - layerResolution*kU.out*kU.in/m
+				uid := u.ID()
+				kU := k[uid]
+				qLayer += weight(uid, uid) - layerResolution*kU.out*kU.in/m
 			}
 			q[l] = layerWeight * qLayer
 			continue
@@ -103,10 +107,12 @@ func qDirectedMultiplex(g DirectedMultiplex, communities [][]graph.Node, weights
 		var qLayer float64
 		for _, c := range communities {
 			for _, u := range c {
-				kU := k[u.ID()]
+				uid := u.ID()
+				kU := k[uid]
 				for _, v := range c {
-					kV := k[v.ID()]
-					qLayer += weight(u, v) - layerResolution*kU.out*kV.in/m
+					vid := v.ID()
+					kV := k[vid]
+					qLayer += weight(uid, vid) - layerResolution*kU.out*kV.in/m
 				}
 			}
 		}
@@ -321,7 +327,7 @@ func reduceDirectedMultiplex(g DirectedMultiplex, communities [][]graph.Node, we
 				continue
 			}
 			var sign float64
-			var weight func(x, y graph.Node) float64
+			var weight func(xid, yid int64) float64
 			if w < 0 {
 				sign, weight = -1, negativeWeightFuncFor(layer)
 			} else {
@@ -332,23 +338,27 @@ func reduceDirectedMultiplex(g DirectedMultiplex, communities [][]graph.Node, we
 
 				var out []int
 				u := n
-				for _, v := range layer.From(u) {
-					vid := communityOf[v.ID()]
-					if vid != id {
-						out = append(out, vid)
+				uid := u.ID()
+				for _, v := range layer.From(uid) {
+					vid := v.ID()
+					vcid := communityOf[vid]
+					if vcid != id {
+						out = append(out, vcid)
 					}
-					r.layers[l].weights[[2]int{id, vid}] = sign * weight(u, v)
+					r.layers[l].weights[[2]int{id, vcid}] = sign * weight(uid, vid)
 				}
 				r.layers[l].edgesFrom[id] = out
 
 				var in []int
 				v := n
-				for _, u := range layer.To(v) {
-					uid := communityOf[u.ID()]
-					if uid != id {
-						in = append(in, uid)
+				vid := v.ID()
+				for _, u := range layer.To(vid) {
+					uid := u.ID()
+					ucid := communityOf[uid]
+					if ucid != id {
+						in = append(in, ucid)
 					}
-					r.layers[l].weights[[2]int{uid, id}] = sign * weight(u, v)
+					r.layers[l].weights[[2]int{ucid, id}] = sign * weight(uid, vid)
 				}
 				r.layers[l].edgesTo[id] = in
 			}
@@ -408,7 +418,7 @@ func reduceDirectedMultiplex(g DirectedMultiplex, communities [][]graph.Node, we
 			continue
 		}
 		var sign float64
-		var weight func(x, y graph.Node) float64
+		var weight func(xid, yid int64) float64
 		if w < 0 {
 			sign, weight = -1, negativeWeightFuncFor(layer)
 		} else {
@@ -418,43 +428,47 @@ func reduceDirectedMultiplex(g DirectedMultiplex, communities [][]graph.Node, we
 			var out, in []int
 			for _, n := range comm {
 				u := n
+				uid := u.ID()
 				for _, v := range comm {
-					r.nodes[id].weights[l] += sign * weight(u, v)
+					r.nodes[id].weights[l] += sign * weight(uid, v.ID())
 				}
 
-				for _, v := range layer.From(u) {
-					vid := communityOf[v.ID()]
+				for _, v := range layer.From(uid) {
+					vid := v.ID()
+					vcid := communityOf[vid]
 					found := false
 					for _, e := range out {
-						if e == vid {
+						if e == vcid {
 							found = true
 							break
 						}
 					}
-					if !found && vid != id {
-						out = append(out, vid)
+					if !found && vcid != id {
+						out = append(out, vcid)
 					}
 					// Add half weights because the other
 					// ends of edges are also counted.
-					r.layers[l].weights[[2]int{id, vid}] += sign * weight(u, v) / 2
+					r.layers[l].weights[[2]int{id, vcid}] += sign * weight(uid, vid) / 2
 				}
 
 				v := n
-				for _, u := range layer.To(v) {
-					uid := communityOf[u.ID()]
+				vid := v.ID()
+				for _, u := range layer.To(vid) {
+					uid := u.ID()
+					ucid := communityOf[uid]
 					found := false
 					for _, e := range in {
-						if e == uid {
+						if e == ucid {
 							found = true
 							break
 						}
 					}
-					if !found && uid != id {
-						in = append(in, uid)
+					if !found && ucid != id {
+						in = append(in, ucid)
 					}
 					// Add half weights because the other
 					// ends of edges are also counted.
-					r.layers[l].weights[[2]int{uid, id}] += sign * weight(u, v) / 2
+					r.layers[l].weights[[2]int{ucid, id}] += sign * weight(uid, vid) / 2
 				}
 
 			}
@@ -478,8 +492,7 @@ type directedLayerHandle struct {
 }
 
 // Has returns whether the node exists within the graph.
-func (g directedLayerHandle) Has(n graph.Node) bool {
-	id := n.ID()
+func (g directedLayerHandle) Has(id int64) bool {
 	return 0 <= id && id < int64(len(g.multiplex.nodes))
 }
 
@@ -493,8 +506,8 @@ func (g directedLayerHandle) Nodes() []graph.Node {
 }
 
 // From returns all nodes in g that can be reached directly from u.
-func (g directedLayerHandle) From(u graph.Node) []graph.Node {
-	out := g.multiplex.layers[g.layer].edgesFrom[u.ID()]
+func (g directedLayerHandle) From(uid int64) []graph.Node {
+	out := g.multiplex.layers[g.layer].edgesFrom[uid]
 	nodes := make([]graph.Node, len(out))
 	for i, vid := range out {
 		nodes[i] = g.multiplex.nodes[vid]
@@ -503,8 +516,8 @@ func (g directedLayerHandle) From(u graph.Node) []graph.Node {
 }
 
 // To returns all nodes in g that can reach directly to v.
-func (g directedLayerHandle) To(v graph.Node) []graph.Node {
-	in := g.multiplex.layers[g.layer].edgesTo[v.ID()]
+func (g directedLayerHandle) To(vid int64) []graph.Node {
+	in := g.multiplex.layers[g.layer].edgesTo[vid]
 	nodes := make([]graph.Node, len(in))
 	for i, uid := range in {
 		nodes[i] = g.multiplex.nodes[uid]
@@ -513,9 +526,7 @@ func (g directedLayerHandle) To(v graph.Node) []graph.Node {
 }
 
 // HasEdgeBetween returns whether an edge exists between nodes x and y.
-func (g directedLayerHandle) HasEdgeBetween(x, y graph.Node) bool {
-	xid := x.ID()
-	yid := y.ID()
+func (g directedLayerHandle) HasEdgeBetween(xid, yid int64) bool {
 	if xid == yid {
 		return false
 	}
@@ -531,9 +542,7 @@ func (g directedLayerHandle) HasEdgeBetween(x, y graph.Node) bool {
 }
 
 // HasEdgeFromTo returns whether an edge exists from node u to v.
-func (g directedLayerHandle) HasEdgeFromTo(u, v graph.Node) bool {
-	uid := u.ID()
-	vid := v.ID()
+func (g directedLayerHandle) HasEdgeFromTo(uid, vid int64) bool {
 	if uid == vid || !isValidID(uid) || !isValidID(vid) {
 		return false
 	}
@@ -543,15 +552,13 @@ func (g directedLayerHandle) HasEdgeFromTo(u, v graph.Node) bool {
 
 // Edge returns the edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g directedLayerHandle) Edge(u, v graph.Node) graph.Edge {
-	return g.WeightedEdge(u, v)
+func (g directedLayerHandle) Edge(uid, vid int64) graph.Edge {
+	return g.WeightedEdge(uid, vid)
 }
 
 // WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g directedLayerHandle) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
-	uid := u.ID()
-	vid := v.ID()
+func (g directedLayerHandle) WeightedEdge(uid, vid int64) graph.WeightedEdge {
 	if uid == vid || !isValidID(uid) || !isValidID(vid) {
 		return nil
 	}
@@ -559,16 +566,14 @@ func (g directedLayerHandle) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
 	if !ok {
 		return nil
 	}
-	return multiplexEdge{from: g.multiplex.nodes[u.ID()], to: g.multiplex.nodes[v.ID()], weight: w}
+	return multiplexEdge{from: g.multiplex.nodes[uid], to: g.multiplex.nodes[vid], weight: w}
 }
 
 // Weight returns the weight for the edge between x and y if Edge(x, y) returns a non-nil Edge.
 // If x and y are the same node the internal node weight is returned. If there is no joining
 // edge between the two nodes the weight value returned is zero. Weight returns true if an edge
 // exists between x and y or if x and y have the same ID, false otherwise.
-func (g directedLayerHandle) Weight(x, y graph.Node) (w float64, ok bool) {
-	xid := x.ID()
-	yid := y.ID()
+func (g directedLayerHandle) Weight(xid, yid int64) (w float64, ok bool) {
 	if !isValidID(xid) || !isValidID(yid) {
 		return 0, false
 	}
@@ -598,7 +603,7 @@ type directedMultiplexLocalMover struct {
 	// that returns the Weight value
 	// of the non-nil edge between x
 	// and y.
-	weight []func(x, y graph.Node) float64
+	weight []func(xid, yid int64) float64
 
 	// communities is the current
 	// division of g.
@@ -648,7 +653,7 @@ func newDirectedMultiplexLocalMover(g *ReducedDirectedMultiplex, communities [][
 		memberships:   make([]int, len(nodes)),
 		resolutions:   resolutions,
 		weights:       weights,
-		weight:        make([]func(x, y graph.Node) float64, g.Depth()),
+		weight:        make([]func(xid, yid int64) float64, g.Depth()),
 	}
 
 	// Calculate the total edge weight of the graph
@@ -656,7 +661,7 @@ func newDirectedMultiplexLocalMover(g *ReducedDirectedMultiplex, communities [][
 	var zero int
 	for i := 0; i < g.Depth(); i++ {
 		l.edgeWeightsOf[i] = make([]directedWeights, len(nodes))
-		var weight func(x, y graph.Node) float64
+		var weight func(xid, yid int64) float64
 
 		if weights != nil {
 			if weights[i] == 0 {
@@ -677,19 +682,22 @@ func newDirectedMultiplexLocalMover(g *ReducedDirectedMultiplex, communities [][
 		layer := g.Layer(i)
 		for _, n := range l.nodes {
 			u := n
+			uid := u.ID()
 			var wOut float64
-			for _, v := range layer.From(u) {
-				wOut += weight(u, v)
+			for _, v := range layer.From(uid) {
+				wOut += weight(uid, v.ID())
 			}
 
 			v := n
+			vid := v.ID()
 			var wIn float64
-			for _, u := range layer.To(v) {
-				wIn += weight(u, v)
+			for _, u := range layer.To(vid) {
+				wIn += weight(u.ID(), vid)
 			}
 
-			w := weight(n, n)
-			l.edgeWeightsOf[i][u.ID()] = directedWeights{out: w + wOut, in: w + wIn}
+			id := n.ID()
+			w := weight(id, id)
+			l.edgeWeightsOf[i][uid] = directedWeights{out: w + wOut, in: w + wIn}
 			l.m[i] += w + wOut
 		}
 		if l.m[i] == 0 {
@@ -836,8 +844,8 @@ func (l *directedMultiplexLocalMover) deltaQ(n graph.Node) (deltaQ float64, dst
 					removal = true
 				}
 
-				k_aC.in += l.weight[layer](n, u)
-				k_aC.out += l.weight[layer](u, n)
+				k_aC.in += l.weight[layer](id, uid)
+				k_aC.out += l.weight[layer](uid, id)
 				// sigma_totC could be kept for each community
 				// and updated for moves, changing the calculation
 				// of sigma_totC here from O(n_c) to O(1), but
@@ -849,7 +857,7 @@ func (l *directedMultiplexLocalMover) deltaQ(n graph.Node) (deltaQ float64, dst
 				sigma_totC.out += w.out
 			}
 
-			a_aa := l.weight[layer](n, n)
+			a_aa := l.weight[layer](id, id)
 			k_a := l.edgeWeightsOf[layer][id]
 			gamma := 1.0
 			if l.resolutions != nil {
diff --git a/graph/community/louvain_directed_multiplex_test.go b/graph/community/louvain_directed_multiplex_test.go
index 5f6082ed..f1523f12 100644
--- a/graph/community/louvain_directed_multiplex_test.go
+++ b/graph/community/louvain_directed_multiplex_test.go
@@ -390,7 +390,7 @@ tests:
 							}
 							layer := g.Layer(l)
 							for n := range c {
-								if layer.HasEdgeBetween(simple.Node(n), target) {
+								if layer.HasEdgeBetween(int64(n), target.ID()) {
 									connected = true
 									break search
 								}
@@ -701,7 +701,7 @@ func directedMultiplexFrom(raw []layer) (DirectedLayers, []float64, error) {
 		g := simple.NewWeightedDirectedGraph(0, 0)
 		for u, e := range l.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
diff --git a/graph/community/louvain_directed_test.go b/graph/community/louvain_directed_test.go
index 3a649791..5f17d2ff 100644
--- a/graph/community/louvain_directed_test.go
+++ b/graph/community/louvain_directed_test.go
@@ -204,7 +204,7 @@ func TestCommunityQDirected(t *testing.T) {
 		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -221,7 +221,7 @@ func TestCommunityQWeightedDirected(t *testing.T) {
 		g := simple.NewWeightedDirectedGraph(0, 0)
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -257,7 +257,7 @@ func TestCommunityDeltaQDirected(t *testing.T) {
 		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -274,7 +274,7 @@ func TestCommunityDeltaQWeightedDirected(t *testing.T) {
 		g := simple.NewWeightedDirectedGraph(0, 0)
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -338,7 +338,7 @@ func testCommunityDeltaQDirected(t *testing.T, test communityDirectedQTest, g gr
 				}
 				connected := false
 				for n := range c {
-					if g.HasEdgeBetween(simple.Node(n), target) {
+					if g.HasEdgeBetween(int64(n), target.ID()) {
 						connected = true
 						break
 					}
@@ -382,7 +382,7 @@ func TestReduceQConsistencyDirected(t *testing.T) {
 		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -399,7 +399,7 @@ func TestReduceQConsistencyWeightedDirected(t *testing.T) {
 		g := simple.NewWeightedDirectedGraph(0, 0)
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -500,7 +500,7 @@ func TestMoveLocalDirected(t *testing.T) {
 		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -517,7 +517,7 @@ func TestMoveLocalWeightedDirected(t *testing.T) {
 		g := simple.NewWeightedDirectedGraph(0, 0)
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -562,7 +562,7 @@ func TestModularizeDirected(t *testing.T) {
 		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -579,7 +579,7 @@ func TestModularizeWeightedDirected(t *testing.T) {
 		g := simple.NewWeightedDirectedGraph(0, 0)
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
diff --git a/graph/community/louvain_undirected.go b/graph/community/louvain_undirected.go
index 838708cb..0f33d3f4 100644
--- a/graph/community/louvain_undirected.go
+++ b/graph/community/louvain_undirected.go
@@ -34,19 +34,21 @@ func qUndirected(g graph.Undirected, communities [][]graph.Node, resolution floa
 	var m2 float64
 	k := make(map[int64]float64, len(nodes))
 	for _, u := range nodes {
-		w := weight(u, u)
-		for _, v := range g.From(u) {
-			w += weight(u, v)
+		uid := u.ID()
+		w := weight(uid, uid)
+		for _, v := range g.From(uid) {
+			w += weight(uid, v.ID())
 		}
 		m2 += w
-		k[u.ID()] = w
+		k[uid] = w
 	}
 
 	if communities == nil {
 		var q float64
 		for _, u := range nodes {
-			kU := k[u.ID()]
-			q += weight(u, u) - resolution*kU*kU/m2
+			uid := u.ID()
+			kU := k[uid]
+			q += weight(uid, uid) - resolution*kU*kU/m2
 		}
 		return q / m2
 	}
@@ -57,10 +59,12 @@ func qUndirected(g graph.Undirected, communities [][]graph.Node, resolution floa
 	var q float64
 	for _, c := range communities {
 		for i, u := range c {
-			kU := k[u.ID()]
-			q += weight(u, u) - resolution*kU*kU/m2
+			uid := u.ID()
+			kU := k[uid]
+			q += weight(uid, uid) - resolution*kU*kU/m2
 			for _, v := range c[i+1:] {
-				q += 2 * (weight(u, v) - resolution*kU*k[v.ID()]/m2)
+				vid := v.ID()
+				q += 2 * (weight(uid, vid) - resolution*kU*k[vid]/m2)
 			}
 		}
 	}
@@ -198,19 +202,21 @@ func reduceUndirected(g graph.Undirected, communities [][]graph.Node) *ReducedUn
 			communityOf[n.ID()] = i
 		}
 		for _, u := range nodes {
+			uid := u.ID()
+			ucid := communityOf[uid]
 			var out []int
-			uid := communityOf[u.ID()]
-			for _, v := range g.From(u) {
-				vid := communityOf[v.ID()]
-				if vid != uid {
-					out = append(out, vid)
+			for _, v := range g.From(uid) {
+				vid := v.ID()
+				vcid := communityOf[vid]
+				if vcid != ucid {
+					out = append(out, vcid)
 				}
-				if uid < vid {
+				if ucid < vcid {
 					// Only store the weight once.
-					r.weights[[2]int{uid, vid}] = weight(u, v)
+					r.weights[[2]int{ucid, vcid}] = weight(uid, vid)
 				}
 			}
-			r.edges[uid] = out
+			r.edges[ucid] = out
 		}
 		return &r
 	}
@@ -254,39 +260,40 @@ func reduceUndirected(g graph.Undirected, communities [][]graph.Node) *ReducedUn
 			communityOf[n.ID()] = i
 		}
 	}
-	for uid, comm := range communities {
+	for ucid, comm := range communities {
 		var out []int
 		for i, u := range comm {
-			r.nodes[uid].weight += weight(u, u)
+			uid := u.ID()
+			r.nodes[ucid].weight += weight(uid, uid)
 			for _, v := range comm[i+1:] {
-				r.nodes[uid].weight += 2 * weight(u, v)
+				r.nodes[ucid].weight += 2 * weight(uid, v.ID())
 			}
-			for _, v := range g.From(u) {
-				vid := communityOf[v.ID()]
+			for _, v := range g.From(uid) {
+				vid := v.ID()
+				vcid := communityOf[vid]
 				found := false
 				for _, e := range out {
-					if e == vid {
+					if e == vcid {
 						found = true
 						break
 					}
 				}
-				if !found && vid != uid {
-					out = append(out, vid)
+				if !found && vcid != ucid {
+					out = append(out, vcid)
 				}
-				if uid < vid {
+				if ucid < vcid {
 					// Only store the weight once.
-					r.weights[[2]int{uid, vid}] += weight(u, v)
+					r.weights[[2]int{ucid, vcid}] += weight(uid, vid)
 				}
 			}
 		}
-		r.edges[uid] = out
+		r.edges[ucid] = out
 	}
 	return &r
 }
 
 // Has returns whether the node exists within the graph.
-func (g *ReducedUndirected) Has(n graph.Node) bool {
-	id := n.ID()
+func (g *ReducedUndirected) Has(id int64) bool {
 	return 0 <= id || id < int64(len(g.nodes))
 }
 
@@ -300,8 +307,8 @@ func (g *ReducedUndirected) Nodes() []graph.Node {
 }
 
 // From returns all nodes in g that can be reached directly from u.
-func (g *ReducedUndirected) From(u graph.Node) []graph.Node {
-	out := g.edges[u.ID()]
+func (g *ReducedUndirected) From(uid int64) []graph.Node {
+	out := g.edges[uid]
 	nodes := make([]graph.Node, len(out))
 	for i, vid := range out {
 		nodes[i] = g.nodes[vid]
@@ -310,9 +317,7 @@ func (g *ReducedUndirected) From(u graph.Node) []graph.Node {
 }
 
 // HasEdgeBetween returns whether an edge exists between nodes x and y.
-func (g *ReducedUndirected) HasEdgeBetween(x, y graph.Node) bool {
-	xid := x.ID()
-	yid := y.ID()
+func (g *ReducedUndirected) HasEdgeBetween(xid, yid int64) bool {
 	if xid == yid || !isValidID(xid) || !isValidID(yid) {
 		return false
 	}
@@ -325,25 +330,23 @@ func (g *ReducedUndirected) HasEdgeBetween(x, y graph.Node) bool {
 
 // Edge returns the edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g *ReducedUndirected) Edge(u, v graph.Node) graph.Edge {
-	return g.WeightedEdgeBetween(u, v)
+func (g *ReducedUndirected) Edge(uid, vid int64) graph.Edge {
+	return g.WeightedEdgeBetween(uid, vid)
 }
 
 // WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g *ReducedUndirected) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
-	return g.WeightedEdgeBetween(u, v)
+func (g *ReducedUndirected) WeightedEdge(uid, vid int64) graph.WeightedEdge {
+	return g.WeightedEdgeBetween(uid, vid)
 }
 
 // EdgeBetween returns the edge between nodes x and y.
-func (g *ReducedUndirected) EdgeBetween(x, y graph.Node) graph.Edge {
-	return g.WeightedEdgeBetween(x, y)
+func (g *ReducedUndirected) EdgeBetween(xid, yid int64) graph.Edge {
+	return g.WeightedEdgeBetween(xid, yid)
 }
 
 // WeightedEdgeBetween returns the weighted edge between nodes x and y.
-func (g *ReducedUndirected) WeightedEdgeBetween(x, y graph.Node) graph.WeightedEdge {
-	xid := x.ID()
-	yid := y.ID()
+func (g *ReducedUndirected) WeightedEdgeBetween(xid, yid int64) graph.WeightedEdge {
 	if xid == yid || !isValidID(xid) || !isValidID(yid) {
 		return nil
 	}
@@ -354,16 +357,14 @@ func (g *ReducedUndirected) WeightedEdgeBetween(x, y graph.Node) graph.WeightedE
 	if !ok {
 		return nil
 	}
-	return edge{from: g.nodes[x.ID()], to: g.nodes[y.ID()], weight: w}
+	return edge{from: g.nodes[xid], to: g.nodes[yid], weight: w}
 }
 
 // Weight returns the weight for the edge between x and y if Edge(x, y) returns a non-nil Edge.
 // If x and y are the same node the internal node weight is returned. If there is no joining
 // edge between the two nodes the weight value returned is zero. Weight returns true if an edge
 // exists between x and y or if x and y have the same ID, false otherwise.
-func (g *ReducedUndirected) Weight(x, y graph.Node) (w float64, ok bool) {
-	xid := x.ID()
-	yid := y.ID()
+func (g *ReducedUndirected) Weight(xid, yid int64) (w float64, ok bool) {
 	if !isValidID(xid) || !isValidID(yid) {
 		return 0, false
 	}
@@ -396,7 +397,7 @@ type undirectedLocalMover struct {
 	// that returns the Weight value
 	// of the non-nil edge between x
 	// and y.
-	weight func(x, y graph.Node) float64
+	weight func(xid, yid int64) float64
 
 	// communities is the current
 	// division of g.
@@ -440,11 +441,12 @@ func newUndirectedLocalMover(g *ReducedUndirected, communities [][]graph.Node, r
 	// Calculate the total edge weight of the graph
 	// and degree weights for each node.
 	for _, u := range l.nodes {
-		w := l.weight(u, u)
-		for _, v := range g.From(u) {
-			w += l.weight(u, v)
+		uid := u.ID()
+		w := l.weight(uid, uid)
+		for _, v := range g.From(uid) {
+			w += l.weight(uid, v.ID())
 		}
-		l.edgeWeightOf[u.ID()] = w
+		l.edgeWeightOf[uid] = w
 		l.m2 += w
 	}
 	if l.m2 == 0 {
@@ -514,7 +516,7 @@ func (l *undirectedLocalMover) move(dst int, src commIdx) {
 // is in communities.
 func (l *undirectedLocalMover) deltaQ(n graph.Node) (deltaQ float64, dst int, src commIdx) {
 	id := n.ID()
-	a_aa := l.weight(n, n)
+	a_aa := l.weight(id, id)
 	k_a := l.edgeWeightOf[id]
 	m2 := l.m2
 	gamma := l.resolution
@@ -559,7 +561,7 @@ func (l *undirectedLocalMover) deltaQ(n graph.Node) (deltaQ float64, dst int, sr
 				removal = true
 			}
 
-			k_aC += l.weight(n, u)
+			k_aC += l.weight(id, uid)
 			// sigma_totC could be kept for each community
 			// and updated for moves, changing the calculation
 			// of sigma_totC here from O(n_c) to O(1), but
diff --git a/graph/community/louvain_undirected_multiplex.go b/graph/community/louvain_undirected_multiplex.go
index 39f51714..794d90dd 100644
--- a/graph/community/louvain_undirected_multiplex.go
+++ b/graph/community/louvain_undirected_multiplex.go
@@ -66,7 +66,7 @@ func qUndirectedMultiplex(g UndirectedMultiplex, communities [][]graph.Node, wei
 			layerResolution = resolutions[l]
 		}
 
-		var weight func(x, y graph.Node) float64
+		var weight func(xid, yid int64) float64
 		if layerWeight < 0 {
 			weight = negativeWeightFuncFor(layer)
 		} else {
@@ -78,19 +78,21 @@ func qUndirectedMultiplex(g UndirectedMultiplex, communities [][]graph.Node, wei
 		var m2 float64
 		k := make(map[int64]float64, len(nodes))
 		for _, u := range nodes {
-			w := weight(u, u)
-			for _, v := range layer.From(u) {
-				w += weight(u, v)
+			uid := u.ID()
+			w := weight(uid, uid)
+			for _, v := range layer.From(uid) {
+				w += weight(uid, v.ID())
 			}
 			m2 += w
-			k[u.ID()] = w
+			k[uid] = w
 		}
 
 		if communities == nil {
 			var qLayer float64
 			for _, u := range nodes {
-				kU := k[u.ID()]
-				qLayer += weight(u, u) - layerResolution*kU*kU/m2
+				uid := u.ID()
+				kU := k[uid]
+				qLayer += weight(uid, uid) - layerResolution*kU*kU/m2
 			}
 			q[l] = layerWeight * qLayer
 			continue
@@ -102,10 +104,12 @@ func qUndirectedMultiplex(g UndirectedMultiplex, communities [][]graph.Node, wei
 		var qLayer float64
 		for _, c := range communities {
 			for i, u := range c {
-				kU := k[u.ID()]
-				qLayer += weight(u, u) - layerResolution*kU*kU/m2
+				uid := u.ID()
+				kU := k[uid]
+				qLayer += weight(uid, uid) - layerResolution*kU*kU/m2
 				for _, v := range c[i+1:] {
-					qLayer += 2 * (weight(u, v) - layerResolution*kU*k[v.ID()]/m2)
+					vid := v.ID()
+					qLayer += 2 * (weight(uid, vid) - layerResolution*kU*k[vid]/m2)
 				}
 			}
 		}
@@ -319,7 +323,7 @@ func reduceUndirectedMultiplex(g UndirectedMultiplex, communities [][]graph.Node
 				continue
 			}
 			var sign float64
-			var weight func(x, y graph.Node) float64
+			var weight func(xid, yid int64) float64
 			if w < 0 {
 				sign, weight = -1, negativeWeightFuncFor(layer)
 			} else {
@@ -327,18 +331,20 @@ func reduceUndirectedMultiplex(g UndirectedMultiplex, communities [][]graph.Node
 			}
 			for _, u := range nodes {
 				var out []int
-				uid := communityOf[u.ID()]
-				for _, v := range layer.From(u) {
-					vid := communityOf[v.ID()]
-					if vid != uid {
-						out = append(out, vid)
+				uid := u.ID()
+				ucid := communityOf[uid]
+				for _, v := range layer.From(uid) {
+					vid := v.ID()
+					vcid := communityOf[vid]
+					if vcid != ucid {
+						out = append(out, vcid)
 					}
-					if uid < vid {
+					if ucid < vcid {
 						// Only store the weight once.
-						r.layers[l].weights[[2]int{uid, vid}] = sign * weight(u, v)
+						r.layers[l].weights[[2]int{ucid, vcid}] = sign * weight(uid, vid)
 					}
 				}
-				r.layers[l].edges[uid] = out
+				r.layers[l].edges[ucid] = out
 			}
 		}
 		return &r
@@ -395,38 +401,40 @@ func reduceUndirectedMultiplex(g UndirectedMultiplex, communities [][]graph.Node
 			continue
 		}
 		var sign float64
-		var weight func(x, y graph.Node) float64
+		var weight func(xid, yid int64) float64
 		if w < 0 {
 			sign, weight = -1, negativeWeightFuncFor(layer)
 		} else {
 			sign, weight = 1, positiveWeightFuncFor(layer)
 		}
-		for uid, comm := range communities {
+		for ucid, comm := range communities {
 			var out []int
 			for i, u := range comm {
-				r.nodes[uid].weights[l] += sign * weight(u, u)
+				uid := u.ID()
+				r.nodes[ucid].weights[l] += sign * weight(uid, uid)
 				for _, v := range comm[i+1:] {
-					r.nodes[uid].weights[l] += 2 * sign * weight(u, v)
+					r.nodes[ucid].weights[l] += 2 * sign * weight(uid, v.ID())
 				}
-				for _, v := range layer.From(u) {
-					vid := communityOf[v.ID()]
+				for _, v := range layer.From(uid) {
+					vid := v.ID()
+					vcid := communityOf[vid]
 					found := false
 					for _, e := range out {
-						if e == vid {
+						if e == vcid {
 							found = true
 							break
 						}
 					}
-					if !found && vid != uid {
-						out = append(out, vid)
+					if !found && vcid != ucid {
+						out = append(out, vcid)
 					}
-					if uid < vid {
+					if ucid < vcid {
 						// Only store the weight once.
-						r.layers[l].weights[[2]int{uid, vid}] += sign * weight(u, v)
+						r.layers[l].weights[[2]int{ucid, vcid}] += sign * weight(uid, vid)
 					}
 				}
 			}
-			r.layers[l].edges[uid] = out
+			r.layers[l].edges[ucid] = out
 		}
 	}
 	return &r
@@ -445,8 +453,7 @@ type undirectedLayerHandle struct {
 }
 
 // Has returns whether the node exists within the graph.
-func (g undirectedLayerHandle) Has(n graph.Node) bool {
-	id := n.ID()
+func (g undirectedLayerHandle) Has(id int64) bool {
 	return 0 <= id && id < int64(len(g.multiplex.nodes))
 }
 
@@ -460,8 +467,8 @@ func (g undirectedLayerHandle) Nodes() []graph.Node {
 }
 
 // From returns all nodes in g that can be reached directly from u.
-func (g undirectedLayerHandle) From(u graph.Node) []graph.Node {
-	out := g.multiplex.layers[g.layer].edges[u.ID()]
+func (g undirectedLayerHandle) From(uid int64) []graph.Node {
+	out := g.multiplex.layers[g.layer].edges[uid]
 	nodes := make([]graph.Node, len(out))
 	for i, vid := range out {
 		nodes[i] = g.multiplex.nodes[vid]
@@ -470,9 +477,7 @@ func (g undirectedLayerHandle) From(u graph.Node) []graph.Node {
 }
 
 // HasEdgeBetween returns whether an edge exists between nodes x and y.
-func (g undirectedLayerHandle) HasEdgeBetween(x, y graph.Node) bool {
-	xid := x.ID()
-	yid := y.ID()
+func (g undirectedLayerHandle) HasEdgeBetween(xid, yid int64) bool {
 	if xid == yid || !isValidID(xid) || !isValidID(yid) {
 		return false
 	}
@@ -485,25 +490,23 @@ func (g undirectedLayerHandle) HasEdgeBetween(x, y graph.Node) bool {
 
 // Edge returns the edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g undirectedLayerHandle) Edge(u, v graph.Node) graph.Edge {
-	return g.WeightedEdgeBetween(u, v)
+func (g undirectedLayerHandle) Edge(uid, vid int64) graph.Edge {
+	return g.WeightedEdgeBetween(uid, vid)
 }
 
 // WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g undirectedLayerHandle) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
-	return g.WeightedEdgeBetween(u, v)
+func (g undirectedLayerHandle) WeightedEdge(uid, vid int64) graph.WeightedEdge {
+	return g.WeightedEdgeBetween(uid, vid)
 }
 
 // EdgeBetween returns the edge between nodes x and y.
-func (g undirectedLayerHandle) EdgeBetween(x, y graph.Node) graph.Edge {
-	return g.WeightedEdgeBetween(x, y)
+func (g undirectedLayerHandle) EdgeBetween(xid, yid int64) graph.Edge {
+	return g.WeightedEdgeBetween(xid, yid)
 }
 
 // WeightedEdgeBetween returns the weighted edge between nodes x and y.
-func (g undirectedLayerHandle) WeightedEdgeBetween(x, y graph.Node) graph.WeightedEdge {
-	xid := x.ID()
-	yid := y.ID()
+func (g undirectedLayerHandle) WeightedEdgeBetween(xid, yid int64) graph.WeightedEdge {
 	if xid == yid || !isValidID(xid) || !isValidID(yid) {
 		return nil
 	}
@@ -514,16 +517,14 @@ func (g undirectedLayerHandle) WeightedEdgeBetween(x, y graph.Node) graph.Weight
 	if !ok {
 		return nil
 	}
-	return multiplexEdge{from: g.multiplex.nodes[x.ID()], to: g.multiplex.nodes[y.ID()], weight: w}
+	return multiplexEdge{from: g.multiplex.nodes[xid], to: g.multiplex.nodes[yid], weight: w}
 }
 
 // Weight returns the weight for the edge between x and y if Edge(x, y) returns a non-nil Edge.
 // If x and y are the same node the internal node weight is returned. If there is no joining
 // edge between the two nodes the weight value returned is zero. Weight returns true if an edge
 // exists between x and y or if x and y have the same ID, false otherwise.
-func (g undirectedLayerHandle) Weight(x, y graph.Node) (w float64, ok bool) {
-	xid := x.ID()
-	yid := y.ID()
+func (g undirectedLayerHandle) Weight(xid, yid int64) (w float64, ok bool) {
 	if !isValidID(xid) || !isValidID(yid) {
 		return 0, false
 	}
@@ -556,7 +557,7 @@ type undirectedMultiplexLocalMover struct {
 	// that returns the Weight value
 	// of the non-nil edge between x
 	// and y.
-	weight []func(x, y graph.Node) float64
+	weight []func(xid, yid int64) float64
 
 	// communities is the current
 	// division of g.
@@ -606,7 +607,7 @@ func newUndirectedMultiplexLocalMover(g *ReducedUndirectedMultiplex, communities
 		memberships:  make([]int, len(nodes)),
 		resolutions:  resolutions,
 		weights:      weights,
-		weight:       make([]func(x, y graph.Node) float64, g.Depth()),
+		weight:       make([]func(xid, yid int64) float64, g.Depth()),
 	}
 
 	// Calculate the total edge weight of the graph
@@ -614,7 +615,7 @@ func newUndirectedMultiplexLocalMover(g *ReducedUndirectedMultiplex, communities
 	var zero int
 	for i := 0; i < g.Depth(); i++ {
 		l.edgeWeightOf[i] = make([]float64, len(nodes))
-		var weight func(x, y graph.Node) float64
+		var weight func(xid, yid int64) float64
 
 		if weights != nil {
 			if weights[i] == 0 {
@@ -634,11 +635,12 @@ func newUndirectedMultiplexLocalMover(g *ReducedUndirectedMultiplex, communities
 		l.weight[i] = weight
 		layer := g.Layer(i)
 		for _, u := range l.nodes {
-			w := weight(u, u)
-			for _, v := range layer.From(u) {
-				w += weight(u, v)
+			uid := u.ID()
+			w := weight(uid, uid)
+			for _, v := range layer.From(uid) {
+				w += weight(uid, v.ID())
 			}
-			l.edgeWeightOf[i][u.ID()] = w
+			l.edgeWeightOf[i][uid] = w
 			l.m2[i] += w
 		}
 		if l.m2[i] == 0 {
@@ -779,7 +781,7 @@ func (l *undirectedMultiplexLocalMover) deltaQ(n graph.Node) (deltaQ float64, ds
 					removal = true
 				}
 
-				k_aC += l.weight[layer](n, u)
+				k_aC += l.weight[layer](id, uid)
 				// sigma_totC could be kept for each community
 				// and updated for moves, changing the calculation
 				// of sigma_totC here from O(n_c) to O(1), but
@@ -789,7 +791,7 @@ func (l *undirectedMultiplexLocalMover) deltaQ(n graph.Node) (deltaQ float64, ds
 				sigma_totC += l.edgeWeightOf[layer][uid]
 			}
 
-			a_aa := l.weight[layer](n, n)
+			a_aa := l.weight[layer](id, id)
 			k_a := l.edgeWeightOf[layer][id]
 			gamma := 1.0
 			if l.resolutions != nil {
diff --git a/graph/community/louvain_undirected_multiplex_test.go b/graph/community/louvain_undirected_multiplex_test.go
index 48e3a355..f4b460eb 100644
--- a/graph/community/louvain_undirected_multiplex_test.go
+++ b/graph/community/louvain_undirected_multiplex_test.go
@@ -359,7 +359,7 @@ tests:
 							}
 							layer := g.Layer(l)
 							for n := range c {
-								if layer.HasEdgeBetween(simple.Node(n), target) {
+								if layer.HasEdgeBetween(int64(n), target.ID()) {
 									connected = true
 									break search
 								}
@@ -670,7 +670,7 @@ func undirectedMultiplexFrom(raw []layer) (UndirectedLayers, []float64, error) {
 		g := simple.NewWeightedUndirectedGraph(0, 0)
 		for u, e := range l.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
diff --git a/graph/community/louvain_undirected_test.go b/graph/community/louvain_undirected_test.go
index bb21aa34..2d95b277 100644
--- a/graph/community/louvain_undirected_test.go
+++ b/graph/community/louvain_undirected_test.go
@@ -267,7 +267,7 @@ func TestCommunityQUndirected(t *testing.T) {
 		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -284,7 +284,7 @@ func TestCommunityQWeightedUndirected(t *testing.T) {
 		g := simple.NewWeightedUndirectedGraph(0, 0)
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -320,7 +320,7 @@ func TestCommunityDeltaQUndirected(t *testing.T) {
 		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -337,7 +337,7 @@ func TestCommunityDeltaQWeightedUndirected(t *testing.T) {
 		g := simple.NewWeightedUndirectedGraph(0, 0)
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -401,7 +401,7 @@ func testCommunityDeltaQUndirected(t *testing.T, test communityUndirectedQTest,
 				}
 				connected := false
 				for n := range c {
-					if g.HasEdgeBetween(simple.Node(n), target) {
+					if g.HasEdgeBetween(int64(n), target.ID()) {
 						connected = true
 						break
 					}
@@ -445,7 +445,7 @@ func TestReduceQConsistencyUndirected(t *testing.T) {
 		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -462,7 +462,7 @@ func TestReduceQConsistencyWeightedUndirected(t *testing.T) {
 		g := simple.NewWeightedUndirectedGraph(0, 0)
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -563,7 +563,7 @@ func TestMoveLocalUndirected(t *testing.T) {
 		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -580,7 +580,7 @@ func TestMoveLocalWeightedUndirected(t *testing.T) {
 		g := simple.NewWeightedUndirectedGraph(0, 0)
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -625,7 +625,7 @@ func TestModularizeUndirected(t *testing.T) {
 		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -642,7 +642,7 @@ func TestModularizeWeightedUndirected(t *testing.T) {
 		g := simple.NewWeightedUndirectedGraph(0, 0)
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
diff --git a/graph/encoding/dot/encode.go b/graph/encoding/dot/encode.go
index 04918402..55b96e31 100644
--- a/graph/encoding/dot/encode.go
+++ b/graph/encoding/dot/encode.go
@@ -151,7 +151,7 @@ func (p *printer) print(g graph.Graph, name string, needsIndent, isSubgraph bool
 		if s, ok := n.(Subgrapher); ok {
 			// If the node is not linked to any other node
 			// the graph needs to be written now.
-			if len(g.From(n)) == 0 {
+			if len(g.From(n.ID())) == 0 {
 				g := s.Subgraph()
 				_, subIsDirected := g.(graph.Directed)
 				if subIsDirected != isDirected {
@@ -182,20 +182,22 @@ func (p *printer) print(g graph.Graph, name string, needsIndent, isSubgraph bool
 
 	havePrintedEdgeHeader := false
 	for _, n := range nodes {
-		to := g.From(n)
+		nid := n.ID()
+		to := g.From(nid)
 		sort.Sort(ordered.ByID(to))
 		for _, t := range to {
+			tid := t.ID()
 			if isDirected {
-				if p.visited[edge{inGraph: name, from: n.ID(), to: t.ID()}] {
+				if p.visited[edge{inGraph: name, from: nid, to: tid}] {
 					continue
 				}
-				p.visited[edge{inGraph: name, from: n.ID(), to: t.ID()}] = true
+				p.visited[edge{inGraph: name, from: nid, to: tid}] = true
 			} else {
-				if p.visited[edge{inGraph: name, from: n.ID(), to: t.ID()}] {
+				if p.visited[edge{inGraph: name, from: nid, to: tid}] {
 					continue
 				}
-				p.visited[edge{inGraph: name, from: n.ID(), to: t.ID()}] = true
-				p.visited[edge{inGraph: name, from: t.ID(), to: n.ID()}] = true
+				p.visited[edge{inGraph: name, from: nid, to: tid}] = true
+				p.visited[edge{inGraph: name, from: tid, to: n.ID()}] = true
 			}
 
 			if !havePrintedEdgeHeader {
@@ -217,7 +219,7 @@ func (p *printer) print(g graph.Graph, name string, needsIndent, isSubgraph bool
 			} else {
 				p.writeNode(n)
 			}
-			e, edgeIsPorter := g.Edge(n, t).(Porter)
+			e, edgeIsPorter := g.Edge(nid, tid).(Porter)
 			if edgeIsPorter {
 				p.writePorts(e.FromPort())
 			}
@@ -242,7 +244,7 @@ func (p *printer) print(g graph.Graph, name string, needsIndent, isSubgraph bool
 				p.writePorts(e.ToPort())
 			}
 
-			if a, ok := g.Edge(n, t).(encoding.Attributer); ok {
+			if a, ok := g.Edge(nid, tid).(encoding.Attributer); ok {
 				p.writeAttributeList(a)
 			}
 
diff --git a/graph/ex/fdpclust/gn.go b/graph/ex/fdpclust/gn.go
index bcb1aad1..b44457e8 100644
--- a/graph/ex/fdpclust/gn.go
+++ b/graph/ex/fdpclust/gn.go
@@ -11,29 +11,29 @@ type GraphNode struct {
 	roots     []*GraphNode
 }
 
-func (g *GraphNode) Has(n graph.Node) bool {
-	if n.ID() == g.id {
+func (g *GraphNode) Has(id int64) bool {
+	if id == g.id {
 		return true
 	}
 
 	visited := map[int64]struct{}{g.id: {}}
 	for _, root := range g.roots {
-		if root.ID() == n.ID() {
+		if root.ID() == id {
 			return true
 		}
 
-		if root.has(n, visited) {
+		if root.has(id, visited) {
 			return true
 		}
 	}
 
 	for _, neigh := range g.neighbors {
-		if neigh.ID() == n.ID() {
+		if neigh.ID() == id {
 			return true
 		}
 
 		if gn, ok := neigh.(*GraphNode); ok {
-			if gn.has(n, visited) {
+			if gn.has(id, visited) {
 				return true
 			}
 		}
@@ -42,18 +42,18 @@ func (g *GraphNode) Has(n graph.Node) bool {
 	return false
 }
 
-func (g *GraphNode) has(n graph.Node, visited map[int64]struct{}) bool {
+func (g *GraphNode) has(id int64, visited map[int64]struct{}) bool {
 	for _, root := range g.roots {
 		if _, ok := visited[root.ID()]; ok {
 			continue
 		}
 
 		visited[root.ID()] = struct{}{}
-		if root.ID() == n.ID() {
+		if root.ID() == id {
 			return true
 		}
 
-		if root.has(n, visited) {
+		if root.has(id, visited) {
 			return true
 		}
 
@@ -65,16 +65,15 @@ func (g *GraphNode) has(n graph.Node, visited map[int64]struct{}) bool {
 		}
 
 		visited[neigh.ID()] = struct{}{}
-		if neigh.ID() == n.ID() {
+		if neigh.ID() == id {
 			return true
 		}
 
 		if gn, ok := neigh.(*GraphNode); ok {
-			if gn.has(n, visited) {
+			if gn.has(id, visited) {
 				return true
 			}
 		}
-
 	}
 
 	return false
@@ -128,8 +127,8 @@ func (g *GraphNode) nodes(list []graph.Node, visited map[int64]struct{}) []graph
 	return list
 }
 
-func (g *GraphNode) From(n graph.Node) []graph.Node {
-	if n.ID() == g.ID() {
+func (g *GraphNode) From(id int64) []graph.Node {
+	if id == g.ID() {
 		return g.neighbors
 	}
 
@@ -137,7 +136,7 @@ func (g *GraphNode) From(n graph.Node) []graph.Node {
 	for _, root := range g.roots {
 		visited[root.ID()] = struct{}{}
 
-		if result := root.findNeighbors(n, visited); result != nil {
+		if result := root.findNeighbors(id, visited); result != nil {
 			return result
 		}
 	}
@@ -146,7 +145,7 @@ func (g *GraphNode) From(n graph.Node) []graph.Node {
 		visited[neigh.ID()] = struct{}{}
 
 		if gn, ok := neigh.(*GraphNode); ok {
-			if result := gn.findNeighbors(n, visited); result != nil {
+			if result := gn.findNeighbors(id, visited); result != nil {
 				return result
 			}
 		}
@@ -155,8 +154,8 @@ func (g *GraphNode) From(n graph.Node) []graph.Node {
 	return nil
 }
 
-func (g *GraphNode) findNeighbors(n graph.Node, visited map[int64]struct{}) []graph.Node {
-	if n.ID() == g.ID() {
+func (g *GraphNode) findNeighbors(id int64, visited map[int64]struct{}) []graph.Node {
+	if id == g.ID() {
 		return g.neighbors
 	}
 
@@ -166,7 +165,7 @@ func (g *GraphNode) findNeighbors(n graph.Node, visited map[int64]struct{}) []gr
 		}
 		visited[root.ID()] = struct{}{}
 
-		if result := root.findNeighbors(n, visited); result != nil {
+		if result := root.findNeighbors(id, visited); result != nil {
 			return result
 		}
 	}
@@ -178,7 +177,7 @@ func (g *GraphNode) findNeighbors(n graph.Node, visited map[int64]struct{}) []gr
 		visited[neigh.ID()] = struct{}{}
 
 		if gn, ok := neigh.(*GraphNode); ok {
-			if result := gn.findNeighbors(n, visited); result != nil {
+			if result := gn.findNeighbors(id, visited); result != nil {
 				return result
 			}
 		}
@@ -187,18 +186,18 @@ func (g *GraphNode) findNeighbors(n graph.Node, visited map[int64]struct{}) []gr
 	return nil
 }
 
-func (g *GraphNode) HasEdgeBetween(u, v graph.Node) bool {
-	return g.EdgeBetween(u, v) != nil
+func (g *GraphNode) HasEdgeBetween(uid, vid int64) bool {
+	return g.EdgeBetween(uid, vid) != nil
 }
 
-func (g *GraphNode) Edge(u, v graph.Node) graph.Edge {
-	return g.EdgeBetween(u, v)
+func (g *GraphNode) Edge(uid, vid int64) graph.Edge {
+	return g.EdgeBetween(uid, vid)
 }
 
-func (g *GraphNode) EdgeBetween(u, v graph.Node) graph.Edge {
-	if u.ID() == g.id || v.ID() == g.id {
+func (g *GraphNode) EdgeBetween(uid, vid int64) graph.Edge {
+	if uid == g.id || vid == g.id {
 		for _, neigh := range g.neighbors {
-			if neigh.ID() == u.ID() || neigh.ID() == v.ID() {
+			if neigh.ID() == uid || neigh.ID() == vid {
 				return simple.Edge{F: g, T: neigh}
 			}
 		}
@@ -208,7 +207,7 @@ func (g *GraphNode) EdgeBetween(u, v graph.Node) graph.Edge {
 	visited := map[int64]struct{}{g.id: {}}
 	for _, root := range g.roots {
 		visited[root.ID()] = struct{}{}
-		if result := root.edgeBetween(u, v, visited); result != nil {
+		if result := root.edgeBetween(uid, vid, visited); result != nil {
 			return result
 		}
 	}
@@ -216,7 +215,7 @@ func (g *GraphNode) EdgeBetween(u, v graph.Node) graph.Edge {
 	for _, neigh := range g.neighbors {
 		visited[neigh.ID()] = struct{}{}
 		if gn, ok := neigh.(*GraphNode); ok {
-			if result := gn.edgeBetween(u, v, visited); result != nil {
+			if result := gn.edgeBetween(uid, vid, visited); result != nil {
 				return result
 			}
 		}
@@ -225,10 +224,10 @@ func (g *GraphNode) EdgeBetween(u, v graph.Node) graph.Edge {
 	return nil
 }
 
-func (g *GraphNode) edgeBetween(u, v graph.Node, visited map[int64]struct{}) graph.Edge {
-	if u.ID() == g.id || v.ID() == g.id {
+func (g *GraphNode) edgeBetween(uid, vid int64, visited map[int64]struct{}) graph.Edge {
+	if uid == g.id || vid == g.id {
 		for _, neigh := range g.neighbors {
-			if neigh.ID() == u.ID() || neigh.ID() == v.ID() {
+			if neigh.ID() == uid || neigh.ID() == vid {
 				return simple.Edge{F: g, T: neigh}
 			}
 		}
@@ -240,7 +239,7 @@ func (g *GraphNode) edgeBetween(u, v graph.Node, visited map[int64]struct{}) gra
 			continue
 		}
 		visited[root.ID()] = struct{}{}
-		if result := root.edgeBetween(u, v, visited); result != nil {
+		if result := root.edgeBetween(uid, vid, visited); result != nil {
 			return result
 		}
 	}
@@ -252,7 +251,7 @@ func (g *GraphNode) edgeBetween(u, v graph.Node, visited map[int64]struct{}) gra
 
 		visited[neigh.ID()] = struct{}{}
 		if gn, ok := neigh.(*GraphNode); ok {
-			if result := gn.edgeBetween(u, v, visited); result != nil {
+			if result := gn.edgeBetween(uid, vid, visited); result != nil {
 				return result
 			}
 		}
diff --git a/graph/graph.go b/graph/graph.go
index 4a3a6379..7c6de2e0 100644
--- a/graph/graph.go
+++ b/graph/graph.go
@@ -27,53 +27,57 @@ type WeightedEdge interface {
 
 // Graph is a generalized graph.
 type Graph interface {
-	// Has returns whether the node exists within the graph.
-	Has(Node) bool
+	// Has returns whether a node with the given ID exists
+	// within the graph.
+	Has(id int64) bool
 
 	// Nodes returns all the nodes in the graph.
 	Nodes() []Node
 
 	// From returns all nodes that can be reached directly
-	// from the given node.
-	From(Node) []Node
+	// from the node with the given ID.
+	From(id int64) []Node
 
 	// HasEdgeBetween returns whether an edge exists between
-	// nodes x and y without considering direction.
-	HasEdgeBetween(x, y Node) bool
+	// nodes with IDs xid and yid without considering direction.
+	HasEdgeBetween(xid, yid int64) bool
 
-	// Edge returns the edge from u to v if such an edge
-	// exists and nil otherwise. The node v must be directly
-	// reachable from u as defined by the From method.
-	Edge(u, v Node) Edge
+	// Edge returns the edge from u to v, with IDs uid and vid,
+	// if such an edge exists and nil otherwise. The node v
+	// must be directly reachable from u as defined by the
+	// From method.
+	Edge(uid, vid int64) Edge
 }
 
 // Weighted is a weighted graph.
 type Weighted interface {
 	Graph
 
-	// WeightedEdge returns the weighted edge from u to v if
-	// such an edge exists and nil otherwise. The node v must
-	// be directly reachable from u as defined by the
-	// From method.
-	WeightedEdge(u, v Node) WeightedEdge
+	// WeightedEdge returns the weighted edge from u to v
+	// with IDs uid and vid if such an edge exists and
+	// nil otherwise. The node v must be directly
+	// reachable from u as defined by the From method.
+	WeightedEdge(uid, vid int64) WeightedEdge
 
 	// Weight returns the weight for the edge between
-	// x and y if Edge(x, y) returns a non-nil Edge.
+	// x and y with IDs xid and yid if Edge(xid, yid)
+	// returns a non-nil Edge.
 	// If x and y are the same node or there is no
 	// joining edge between the two nodes the weight
 	// value returned is implementation dependent.
 	// Weight returns true if an edge exists between
 	// x and y or if x and y have the same ID, false
 	// otherwise.
-	Weight(x, y Node) (w float64, ok bool)
+	Weight(xid, yid int64) (w float64, ok bool)
 }
 
 // Undirected is an undirected graph.
 type Undirected interface {
 	Graph
 
-	// EdgeBetween returns the edge between nodes x and y.
-	EdgeBetween(x, y Node) Edge
+	// EdgeBetween returns the edge between nodes x and y
+	// with IDs xid and yid.
+	EdgeBetween(xid, yid int64) Edge
 }
 
 // WeightedUndirected is a weighted undirected graph.
@@ -81,8 +85,8 @@ type WeightedUndirected interface {
 	Weighted
 
 	// WeightedEdgeBetween returns the edge between nodes
-	// x and y.
-	WeightedEdgeBetween(x, y Node) WeightedEdge
+	// x and y with IDs xid and yid.
+	WeightedEdgeBetween(xid, yid int64) WeightedEdge
 }
 
 // Directed is a directed graph.
@@ -90,12 +94,12 @@ type Directed interface {
 	Graph
 
 	// HasEdgeFromTo returns whether an edge exists
-	// in the graph from u to v.
-	HasEdgeFromTo(u, v Node) bool
+	// in the graph from u to v with IDs uid and vid.
+	HasEdgeFromTo(uid, vid int64) bool
 
 	// To returns all nodes that can reach directly
-	// to the given node.
-	To(Node) []Node
+	// to the node with the given ID.
+	To(id int64) []Node
 }
 
 // WeightedDirected is a weighted directed graph.
@@ -103,12 +107,13 @@ type WeightedDirected interface {
 	Weighted
 
 	// HasEdgeFromTo returns whether an edge exists
-	// in the graph from u to v.
-	HasEdgeFromTo(u, v Node) bool
+	// in the graph from u to v with the IDs uid and
+	// vid.
+	HasEdgeFromTo(uid, vid int64) bool
 
 	// To returns all nodes that can reach directly
-	// to the given node.
-	To(Node) []Node
+	// to the node with the given ID.
+	To(id int64) []Node
 }
 
 // NodeAdder is an interface for adding arbitrary nodes to a graph.
@@ -217,7 +222,7 @@ func Copy(dst Builder, src Graph) {
 		dst.AddNode(n)
 	}
 	for _, u := range nodes {
-		for _, v := range src.From(u) {
+		for _, v := range src.From(u.ID()) {
 			dst.SetEdge(dst.NewEdge(u, v))
 		}
 	}
@@ -240,8 +245,8 @@ func CopyWeighted(dst WeightedBuilder, src Weighted) {
 		dst.AddNode(n)
 	}
 	for _, u := range nodes {
-		for _, v := range src.From(u) {
-			dst.SetWeightedEdge(dst.NewWeightedEdge(u, v, src.WeightedEdge(u, v).Weight()))
+		for _, v := range src.From(u.ID()) {
+			dst.SetWeightedEdge(dst.NewWeightedEdge(u, v, src.WeightedEdge(u.ID(), v.ID()).Weight()))
 		}
 	}
 }
diff --git a/graph/graph_test.go b/graph/graph_test.go
index 5a7ce337..47b671f8 100644
--- a/graph/graph_test.go
+++ b/graph/graph_test.go
@@ -273,8 +273,8 @@ func same(a, b graph.Graph) bool {
 		}
 	}
 	for _, u := range a.Nodes() {
-		aFromU := a.From(u)
-		bFromU := b.From(u)
+		aFromU := a.From(u.ID())
+		bFromU := b.From(u.ID())
 		if len(aFromU) != len(bFromU) {
 			return false
 		}
@@ -288,7 +288,7 @@ func same(a, b graph.Graph) bool {
 			aW, aWok := a.(graph.Weighted)
 			bW, bWok := b.(graph.Weighted)
 			if aWok && bWok {
-				if aW.WeightedEdge(u, va).Weight() != bW.WeightedEdge(u, vb).Weight() {
+				if aW.WeightedEdge(u.ID(), va.ID()).Weight() != bW.WeightedEdge(u.ID(), vb.ID()).Weight() {
 					return false
 				}
 			}
diff --git a/graph/graphs/gen/batagelj_brandes.go b/graph/graphs/gen/batagelj_brandes.go
index ce3ec5f9..8238233a 100644
--- a/graph/graphs/gen/batagelj_brandes.go
+++ b/graph/graphs/gen/batagelj_brandes.go
@@ -36,7 +36,7 @@ func Gnp(dst GraphBuilder, n int, p float64, src *rand.Rand) error {
 	}
 
 	for i := 0; i < n; i++ {
-		if !dst.Has(simple.Node(i)) {
+		if !dst.Has(int64(i)) {
 			dst.AddNode(simple.Node(i))
 		}
 	}
@@ -112,7 +112,7 @@ func Gnm(dst GraphBuilder, n, m int, src *rand.Rand) error {
 	}
 
 	for i := 0; i < n; i++ {
-		if !dst.Has(simple.Node(i)) {
+		if !dst.Has(int64(i)) {
 			dst.AddNode(simple.Node(i))
 		}
 	}
@@ -122,7 +122,7 @@ func Gnm(dst GraphBuilder, n, m int, src *rand.Rand) error {
 		for {
 			v, w := edgeNodesFor(rnd(nChoose2))
 			e := simple.Edge{F: w, T: v}
-			if !hasEdge(e.F, e.T) {
+			if !hasEdge(e.F.ID(), e.T.ID()) {
 				dst.SetEdge(e)
 				break
 			}
@@ -137,7 +137,7 @@ func Gnm(dst GraphBuilder, n, m int, src *rand.Rand) error {
 		for {
 			v, w := edgeNodesFor(rnd(nChoose2))
 			e := simple.Edge{F: v, T: w}
-			if !hasEdge(e.F, e.T) {
+			if !hasEdge(e.F.ID(), e.T.ID()) {
 				dst.SetEdge(e)
 				break
 			}
@@ -182,7 +182,7 @@ func SmallWorldsBB(dst GraphBuilder, n, d int, p float64, src *rand.Rand) error
 	}
 
 	for i := 0; i < n; i++ {
-		if !dst.Has(simple.Node(i)) {
+		if !dst.Has(int64(i)) {
 			dst.AddNode(simple.Node(i))
 		}
 	}
@@ -201,14 +201,14 @@ func SmallWorldsBB(dst GraphBuilder, n, d int, p float64, src *rand.Rand) error
 				j := v*(v-1)/2 + (v+i)%n
 				var ej simple.Edge
 				ej.T, ej.F = edgeNodesFor(j)
-				if !hasEdge(ej.From(), ej.To()) {
+				if !hasEdge(ej.From().ID(), ej.To().ID()) {
 					dst.SetEdge(ej)
 				}
 				k--
 				m++
 				var em simple.Edge
 				em.T, em.F = edgeNodesFor(m)
-				if !hasEdge(em.From(), em.To()) {
+				if !hasEdge(em.From().ID(), em.To().ID()) {
 					replace[j] = m
 				} else {
 					replace[j] = replace[m]
@@ -222,17 +222,17 @@ func SmallWorldsBB(dst GraphBuilder, n, d int, p float64, src *rand.Rand) error
 		r := rndN(nChoose2-i) + i
 		var er simple.Edge
 		er.T, er.F = edgeNodesFor(r)
-		if !hasEdge(er.From(), er.To()) {
+		if !hasEdge(er.From().ID(), er.To().ID()) {
 			dst.SetEdge(er)
 		} else {
 			er.T, er.F = edgeNodesFor(replace[r])
-			if !hasEdge(er.From(), er.To()) {
+			if !hasEdge(er.From().ID(), er.To().ID()) {
 				dst.SetEdge(er)
 			}
 		}
 		var ei simple.Edge
 		ei.T, ei.F = edgeNodesFor(i)
-		if !hasEdge(ei.From(), ei.To()) {
+		if !hasEdge(ei.From().ID(), ei.To().ID()) {
 			replace[r] = i
 		} else {
 			replace[r] = replace[i]
@@ -252,12 +252,12 @@ func SmallWorldsBB(dst GraphBuilder, n, d int, p float64, src *rand.Rand) error
 				j := v*(v-1)/2 + (v+i)%n
 				var ej simple.Edge
 				ej.F, ej.T = edgeNodesFor(j)
-				if !hasEdge(ej.From(), ej.To()) {
+				if !hasEdge(ej.From().ID(), ej.To().ID()) {
 					dst.SetEdge(ej)
 				}
 				k--
 				m++
-				if !hasEdge(edgeNodesFor(m)) {
+				if u, v := edgeNodesFor(m); !hasEdge(u.ID(), v.ID()) {
 					replace[j] = m
 				} else {
 					replace[j] = replace[m]
@@ -271,15 +271,15 @@ func SmallWorldsBB(dst GraphBuilder, n, d int, p float64, src *rand.Rand) error
 		r := rndN(nChoose2-i) + i
 		var er simple.Edge
 		er.F, er.T = edgeNodesFor(r)
-		if !hasEdge(er.From(), er.To()) {
+		if !hasEdge(er.From().ID(), er.To().ID()) {
 			dst.SetEdge(er)
 		} else {
 			er.F, er.T = edgeNodesFor(replace[r])
-			if !hasEdge(er.From(), er.To()) {
+			if !hasEdge(er.From().ID(), er.To().ID()) {
 				dst.SetEdge(er)
 			}
 		}
-		if !hasEdge(edgeNodesFor(i)) {
+		if u, v := edgeNodesFor(i); !hasEdge(u.ID(), v.ID()) {
 			replace[r] = i
 		} else {
 			replace[r] = replace[i]
diff --git a/graph/graphs/gen/batagelj_brandes_test.go b/graph/graphs/gen/batagelj_brandes_test.go
index 393f877c..390ab1dd 100644
--- a/graph/graphs/gen/batagelj_brandes_test.go
+++ b/graph/graphs/gen/batagelj_brandes_test.go
@@ -27,7 +27,7 @@ func (g *gnUndirected) SetEdge(e graph.Edge) {
 		return
 	case e.From().ID() > e.To().ID():
 		g.addBackwards = true
-	case g.UndirectedBuilder.HasEdgeBetween(e.From(), e.To()):
+	case g.UndirectedBuilder.HasEdgeBetween(e.From().ID(), e.To().ID()):
 		g.addMultipleEdge = true
 	}
 
@@ -45,7 +45,7 @@ func (g *gnDirected) SetEdge(e graph.Edge) {
 	case e.From().ID() == e.To().ID():
 		g.addSelfLoop = true
 		return
-	case g.DirectedBuilder.HasEdgeFromTo(e.From(), e.To()):
+	case g.DirectedBuilder.HasEdgeFromTo(e.From().ID(), e.To().ID()):
 		g.addMultipleEdge = true
 	}
 
@@ -190,9 +190,10 @@ func TestPowerLawUndirected(t *testing.T) {
 			}
 
 			for _, u := range nodes {
+				uid := u.ID()
 				var lines int
-				for _, v := range g.From(u) {
-					lines += len(g.Lines(u, v))
+				for _, v := range g.From(uid) {
+					lines += len(g.Lines(uid, v.ID()))
 				}
 				if lines < d {
 					t.Errorf("unexpected degree below d: n=%d, d=%d: got:%d", n, d, lines)
@@ -218,9 +219,10 @@ func TestPowerLawDirected(t *testing.T) {
 			}
 
 			for _, u := range nodes {
+				uid := u.ID()
 				var lines int
-				for _, v := range g.From(u) {
-					lines += len(g.Lines(u, v))
+				for _, v := range g.From(uid) {
+					lines += len(g.Lines(uid, v.ID()))
 				}
 				if lines < d {
 					t.Errorf("unexpected degree below d: n=%d, d=%d: got:%d", n, d, lines)
@@ -265,9 +267,10 @@ func TestBipartitePowerLawUndirected(t *testing.T) {
 			}
 
 			for _, u := range nodes {
+				uid := u.ID()
 				var lines int
-				for _, v := range g.From(u) {
-					lines += len(g.Lines(u, v))
+				for _, v := range g.From(uid) {
+					lines += len(g.Lines(uid, v.ID()))
 				}
 				if lines < d {
 					t.Errorf("unexpected degree below d: n=%d, d=%d: got:%d", n, d, lines)
@@ -312,9 +315,10 @@ func TestBipartitePowerLawDirected(t *testing.T) {
 			}
 
 			for _, u := range nodes {
+				uid := u.ID()
 				var lines int
-				for _, v := range g.From(u) {
-					lines += len(g.Lines(u, v))
+				for _, v := range g.From(uid) {
+					lines += len(g.Lines(uid, v.ID()))
 				}
 				if lines < d {
 					t.Errorf("unexpected degree below d: n=%d, d=%d: got:%d", n, d, lines)
diff --git a/graph/graphs/gen/duplication.go b/graph/graphs/gen/duplication.go
index a59889a0..86558cf3 100644
--- a/graph/graphs/gen/duplication.go
+++ b/graph/graphs/gen/duplication.go
@@ -66,6 +66,7 @@ func Duplication(dst UndirectedMutator, n int, delta, alpha, sigma float64, src
 	for i := 0; i < n; i++ {
 		u := nodes[rndN(len(nodes))]
 		d := dst.NewNode()
+		did := d.ID()
 
 		// Add the duplicate node.
 		dst.AddNode(d)
@@ -74,13 +75,14 @@ func Duplication(dst UndirectedMutator, n int, delta, alpha, sigma float64, src
 		// into the rest of the graph.
 		for {
 			// Add edges to parent's neighbours.
-			to := dst.From(u)
+			to := dst.From(u.ID())
 			sort.Sort(ordered.ByID(to))
 			for _, v := range to {
-				if rnd() < delta || dst.HasEdgeBetween(v, d) {
+				vid := v.ID()
+				if rnd() < delta || dst.HasEdgeBetween(vid, did) {
 					continue
 				}
-				if v.ID() < d.ID() {
+				if vid < did {
 					dst.SetEdge(dst.NewEdge(v, d))
 				} else {
 					dst.SetEdge(dst.NewEdge(d, v))
@@ -90,11 +92,13 @@ func Duplication(dst UndirectedMutator, n int, delta, alpha, sigma float64, src
 			// Add edges to old nodes.
 			scaledAlpha := alpha / float64(len(nodes))
 			for _, v := range nodes {
-				switch v.ID() {
-				case u.ID():
+				uid := u.ID()
+				vid := v.ID()
+				switch vid {
+				case uid:
 					if !math.IsNaN(sigma) {
 						if i == 0 || rnd() < sigma {
-							if v.ID() < d.ID() {
+							if vid < did {
 								dst.SetEdge(dst.NewEdge(v, d))
 							} else {
 								dst.SetEdge(dst.NewEdge(d, v))
@@ -104,8 +108,8 @@ func Duplication(dst UndirectedMutator, n int, delta, alpha, sigma float64, src
 					}
 					fallthrough
 				default:
-					if rnd() < scaledAlpha && !dst.HasEdgeBetween(v, d) {
-						if v.ID() < d.ID() {
+					if rnd() < scaledAlpha && !dst.HasEdgeBetween(vid, did) {
+						if vid < did {
 							dst.SetEdge(dst.NewEdge(v, d))
 						} else {
 							dst.SetEdge(dst.NewEdge(d, v))
@@ -114,7 +118,7 @@ func Duplication(dst UndirectedMutator, n int, delta, alpha, sigma float64, src
 				}
 			}
 
-			if len(dst.From(d)) != 0 {
+			if len(dst.From(did)) != 0 {
 				break
 			}
 		}
diff --git a/graph/graphs/gen/duplication_test.go b/graph/graphs/gen/duplication_test.go
index cebf36a5..ae28b8d2 100644
--- a/graph/graphs/gen/duplication_test.go
+++ b/graph/graphs/gen/duplication_test.go
@@ -25,7 +25,7 @@ func (g *duplication) SetEdge(e graph.Edge) {
 		return
 	case e.From().ID() > e.To().ID():
 		g.addBackwards = true
-	case g.UndirectedMutator.HasEdgeBetween(e.From(), e.To()):
+	case g.UndirectedMutator.HasEdgeBetween(e.From().ID(), e.To().ID()):
 		g.addMultipleEdge = true
 	}
 
diff --git a/graph/graphs/gen/gen.go b/graph/graphs/gen/gen.go
index ec724bae..61c3c793 100644
--- a/graph/graphs/gen/gen.go
+++ b/graph/graphs/gen/gen.go
@@ -8,8 +8,8 @@ import "gonum.org/v1/gonum/graph"
 
 // GraphBuilder is a graph that can have nodes and edges added.
 type GraphBuilder interface {
-	Has(graph.Node) bool
-	HasEdgeBetween(x, y graph.Node) bool
+	Has(id int64) bool
+	HasEdgeBetween(xid, yid int64) bool
 	graph.Builder
 }
 
diff --git a/graph/graphs/gen/holme_kim.go b/graph/graphs/gen/holme_kim.go
index 3c929970..351aa85a 100644
--- a/graph/graphs/gen/holme_kim.go
+++ b/graph/graphs/gen/holme_kim.go
@@ -47,7 +47,7 @@ func TunableClusteringScaleFree(dst graph.UndirectedBuilder, n, m int, p float64
 	// Initial condition.
 	wt := make([]float64, n)
 	for u := 0; u < m; u++ {
-		if !dst.Has(simple.Node(u)) {
+		if !dst.Has(int64(0)) {
 			dst.AddNode(simple.Node(u))
 		}
 		// We need to give equal probability for
@@ -68,9 +68,9 @@ func TunableClusteringScaleFree(dst graph.UndirectedBuilder, n, m int, p float64
 		for i := 0; i < m; i++ {
 			// Triad formation.
 			if i != 0 && rnd() < p {
-				for _, w := range permute(dst.From(simple.Node(u)), rndN) {
+				for _, w := range permute(dst.From(int64(u)), rndN) {
 					wid := w.ID()
-					if wid == int64(v) || dst.HasEdgeBetween(w, simple.Node(v)) {
+					if wid == int64(v) || dst.HasEdgeBetween(wid, int64(v)) {
 						continue
 					}
 					dst.SetEdge(simple.Edge{F: w, T: simple.Node(v)})
@@ -87,7 +87,7 @@ func TunableClusteringScaleFree(dst graph.UndirectedBuilder, n, m int, p float64
 				if !ok {
 					return errors.New("gen: depleted distribution")
 				}
-				if u == v || dst.HasEdgeBetween(simple.Node(u), simple.Node(v)) {
+				if u == v || dst.HasEdgeBetween(int64(u), int64(v)) {
 					continue
 				}
 				dst.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
@@ -128,7 +128,7 @@ func PreferentialAttachment(dst graph.UndirectedBuilder, n, m int, src *rand.Ran
 	// Initial condition.
 	wt := make([]float64, n)
 	for u := 0; u < m; u++ {
-		if !dst.Has(simple.Node(u)) {
+		if !dst.Has(int64(u)) {
 			dst.AddNode(simple.Node(u))
 		}
 		// We need to give equal probability for
diff --git a/graph/graphs/gen/small_world.go b/graph/graphs/gen/small_world.go
index b19faf3b..1c6565da 100644
--- a/graph/graphs/gen/small_world.go
+++ b/graph/graphs/gen/small_world.go
@@ -40,7 +40,7 @@ func NavigableSmallWorld(dst GraphBuilder, dims []int, p, q int, r float64, src
 		n *= d
 	}
 	for i := 0; i < n; i++ {
-		if !dst.Has(simple.Node(i)) {
+		if !dst.Has(int64(i)) {
 			dst.AddNode(simple.Node(i))
 		}
 	}
@@ -67,14 +67,14 @@ func NavigableSmallWorld(dst GraphBuilder, dims []int, p, q int, r float64, src
 			if uid > vid {
 				e.F, e.T = e.T, e.F
 			}
-			if !hasEdge(e.From(), e.To()) {
+			if !hasEdge(e.From().ID(), e.To().ID()) {
 				dst.SetEdge(e)
 			}
 			if !isDirected {
 				return
 			}
 			e.F, e.T = e.T, e.F
-			if !hasEdge(e.From(), e.To()) {
+			if !hasEdge(e.From().ID(), e.To().ID()) {
 				dst.SetEdge(e)
 			}
 		})
@@ -110,7 +110,7 @@ func NavigableSmallWorld(dst GraphBuilder, dims []int, p, q int, r float64, src
 			if !isDirected && uid > vid {
 				e.F, e.T = e.T, e.F
 			}
-			if !hasEdge(e.From(), e.To()) {
+			if !hasEdge(e.From().ID(), e.To().ID()) {
 				dst.SetEdge(e)
 			}
 		}
diff --git a/graph/multi/directed.go b/graph/multi/directed.go
index 92143eb4..8da3cfc5 100644
--- a/graph/multi/directed.go
+++ b/graph/multi/directed.go
@@ -103,13 +103,13 @@ func (g *DirectedGraph) SetLine(l graph.Line) {
 		lid  = l.ID()
 	)
 
-	if !g.Has(from) {
+	if !g.Has(fid) {
 		g.AddNode(from)
 	}
 	if g.from[fid][tid] == nil {
 		g.from[fid][tid] = make(map[int64]graph.Line)
 	}
-	if !g.Has(to) {
+	if !g.Has(tid) {
 		g.AddNode(to)
 	}
 	if g.to[tid][fid] == nil {
@@ -149,8 +149,8 @@ func (g *DirectedGraph) Node(id int64) graph.Node {
 }
 
 // Has returns whether the node exists within the graph.
-func (g *DirectedGraph) Has(n graph.Node) bool {
-	_, ok := g.nodes[n.ID()]
+func (g *DirectedGraph) Has(id int64) bool {
+	_, ok := g.nodes[id]
 	return ok
 }
 
@@ -187,30 +187,30 @@ func (g *DirectedGraph) Edges() []graph.Edge {
 }
 
 // From returns all nodes in g that can be reached directly from n.
-func (g *DirectedGraph) From(n graph.Node) []graph.Node {
-	if _, ok := g.from[n.ID()]; !ok {
+func (g *DirectedGraph) From(id int64) []graph.Node {
+	if _, ok := g.from[id]; !ok {
 		return nil
 	}
 
-	from := make([]graph.Node, len(g.from[n.ID()]))
+	from := make([]graph.Node, len(g.from[id]))
 	i := 0
-	for id := range g.from[n.ID()] {
-		from[i] = g.nodes[id]
+	for vid := range g.from[id] {
+		from[i] = g.nodes[vid]
 		i++
 	}
 	return from
 }
 
 // To returns all nodes in g that can reach directly to n.
-func (g *DirectedGraph) To(n graph.Node) []graph.Node {
-	if _, ok := g.from[n.ID()]; !ok {
+func (g *DirectedGraph) To(id int64) []graph.Node {
+	if _, ok := g.from[id]; !ok {
 		return nil
 	}
 
-	to := make([]graph.Node, len(g.to[n.ID()]))
+	to := make([]graph.Node, len(g.to[id]))
 	i := 0
-	for id := range g.to[n.ID()] {
-		to[i] = g.nodes[id]
+	for uid := range g.to[id] {
+		to[i] = g.nodes[uid]
 		i++
 	}
 	return to
@@ -218,9 +218,7 @@ func (g *DirectedGraph) To(n graph.Node) []graph.Node {
 
 // HasEdgeBetween returns whether an edge exists between nodes x and y without
 // considering direction.
-func (g *DirectedGraph) HasEdgeBetween(x, y graph.Node) bool {
-	xid := x.ID()
-	yid := y.ID()
+func (g *DirectedGraph) HasEdgeBetween(xid, yid int64) bool {
 	if _, ok := g.from[xid][yid]; ok {
 		return true
 	}
@@ -231,8 +229,8 @@ func (g *DirectedGraph) HasEdgeBetween(x, y graph.Node) bool {
 // Edge returns the edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
 // The returned graph.Edge is a multi.Edge if an edge exists.
-func (g *DirectedGraph) Edge(u, v graph.Node) graph.Edge {
-	lines := g.Lines(u, v)
+func (g *DirectedGraph) Edge(uid, vid int64) graph.Edge {
+	lines := g.Lines(uid, vid)
 	if len(lines) == 0 {
 		return nil
 	}
@@ -241,8 +239,8 @@ func (g *DirectedGraph) Edge(u, v graph.Node) graph.Edge {
 
 // Lines returns the lines from u to v if such any such lines exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g *DirectedGraph) Lines(u, v graph.Node) []graph.Line {
-	edge := g.from[u.ID()][v.ID()]
+func (g *DirectedGraph) Lines(uid, vid int64) []graph.Line {
+	edge := g.from[uid][vid]
 	if len(edge) == 0 {
 		return nil
 	}
@@ -254,21 +252,21 @@ func (g *DirectedGraph) Lines(u, v graph.Node) []graph.Line {
 }
 
 // HasEdgeFromTo returns whether an edge exists in the graph from u to v.
-func (g *DirectedGraph) HasEdgeFromTo(u, v graph.Node) bool {
-	_, ok := g.from[u.ID()][v.ID()]
+func (g *DirectedGraph) HasEdgeFromTo(uid, vid int64) bool {
+	_, ok := g.from[uid][vid]
 	return ok
 }
 
 // Degree returns the in+out degree of n in g.
-func (g *DirectedGraph) Degree(n graph.Node) int {
-	if _, ok := g.nodes[n.ID()]; !ok {
+func (g *DirectedGraph) Degree(id int64) int {
+	if _, ok := g.nodes[id]; !ok {
 		return 0
 	}
 	var deg int
-	for _, e := range g.from[n.ID()] {
+	for _, e := range g.from[id] {
 		deg += len(e)
 	}
-	for _, e := range g.to[n.ID()] {
+	for _, e := range g.to[id] {
 		deg += len(e)
 	}
 	return deg
diff --git a/graph/multi/directed_test.go b/graph/multi/directed_test.go
index c25a6c7f..487ec9a8 100644
--- a/graph/multi/directed_test.go
+++ b/graph/multi/directed_test.go
@@ -21,7 +21,7 @@ var (
 func TestEdgeOvercounting(t *testing.T) {
 	g := generateDummyGraph()
 
-	if neigh := g.From(Node(Node(2))); len(neigh) != 2 {
+	if neigh := g.From(int64(2)); len(neigh) != 2 {
 		t.Errorf("Node 2 has incorrect number of neighbors got neighbors %v (count %d), expected 2 neighbors {0,1}", neigh, len(neigh))
 	}
 }
diff --git a/graph/multi/undirected.go b/graph/multi/undirected.go
index fedd7162..fb2343a1 100644
--- a/graph/multi/undirected.go
+++ b/graph/multi/undirected.go
@@ -95,13 +95,13 @@ func (g *UndirectedGraph) SetLine(l graph.Line) {
 		lid  = l.ID()
 	)
 
-	if !g.Has(from) {
+	if !g.Has(fid) {
 		g.AddNode(from)
 	}
 	if g.lines[fid][tid] == nil {
 		g.lines[fid][tid] = make(map[int64]graph.Line)
 	}
-	if !g.Has(to) {
+	if !g.Has(tid) {
 		g.AddNode(to)
 	}
 	if g.lines[tid][fid] == nil {
@@ -138,8 +138,8 @@ func (g *UndirectedGraph) Node(id int64) graph.Node {
 }
 
 // Has returns whether the node exists within the graph.
-func (g *UndirectedGraph) Has(n graph.Node) bool {
-	_, ok := g.nodes[n.ID()]
+func (g *UndirectedGraph) Has(id int64) bool {
+	_, ok := g.nodes[id]
 	return ok
 }
 
@@ -185,14 +185,14 @@ func (g *UndirectedGraph) Edges() []graph.Edge {
 }
 
 // From returns all nodes in g that can be reached directly from n.
-func (g *UndirectedGraph) From(n graph.Node) []graph.Node {
-	if !g.Has(n) {
+func (g *UndirectedGraph) From(id int64) []graph.Node {
+	if !g.Has(id) {
 		return nil
 	}
 
-	nodes := make([]graph.Node, len(g.lines[n.ID()]))
+	nodes := make([]graph.Node, len(g.lines[id]))
 	i := 0
-	for from := range g.lines[n.ID()] {
+	for from := range g.lines[id] {
 		nodes[i] = g.nodes[from]
 		i++
 	}
@@ -200,21 +200,21 @@ func (g *UndirectedGraph) From(n graph.Node) []graph.Node {
 }
 
 // HasEdgeBetween returns whether an edge exists between nodes x and y.
-func (g *UndirectedGraph) HasEdgeBetween(x, y graph.Node) bool {
-	_, ok := g.lines[x.ID()][y.ID()]
+func (g *UndirectedGraph) HasEdgeBetween(xid, yid int64) bool {
+	_, ok := g.lines[xid][yid]
 	return ok
 }
 
 // EdgeBetween returns the edge between nodes x and y.
-func (g *UndirectedGraph) EdgeBetween(x, y graph.Node) graph.Edge {
-	return g.Edge(x, y)
+func (g *UndirectedGraph) EdgeBetween(xid, yid int64) graph.Edge {
+	return g.Edge(xid, yid)
 }
 
 // Edge returns the edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
 // The returned graph.Edge is a multi.Edge if an edge exists.
-func (g *UndirectedGraph) Edge(u, v graph.Node) graph.Edge {
-	lines := g.LinesBetween(u, v)
+func (g *UndirectedGraph) Edge(uid, vid int64) graph.Edge {
+	lines := g.LinesBetween(uid, vid)
 	if len(lines) == 0 {
 		return nil
 	}
@@ -223,26 +223,26 @@ func (g *UndirectedGraph) Edge(u, v graph.Node) graph.Edge {
 
 // Lines returns the lines from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g *UndirectedGraph) Lines(u, v graph.Node) []graph.Line {
-	return g.LinesBetween(u, v)
+func (g *UndirectedGraph) Lines(uid, vid int64) []graph.Line {
+	return g.LinesBetween(uid, vid)
 }
 
 // LinesBetween returns the lines between nodes x and y.
-func (g *UndirectedGraph) LinesBetween(x, y graph.Node) []graph.Line {
+func (g *UndirectedGraph) LinesBetween(xid, yid int64) []graph.Line {
 	var lines []graph.Line
-	for _, l := range g.lines[x.ID()][y.ID()] {
+	for _, l := range g.lines[xid][yid] {
 		lines = append(lines, l)
 	}
 	return lines
 }
 
 // Degree returns the degree of n in g.
-func (g *UndirectedGraph) Degree(n graph.Node) int {
-	if _, ok := g.nodes[n.ID()]; !ok {
+func (g *UndirectedGraph) Degree(id int64) int {
+	if _, ok := g.nodes[id]; !ok {
 		return 0
 	}
 	var deg int
-	for _, e := range g.lines[n.ID()] {
+	for _, e := range g.lines[id] {
 		deg += len(e)
 	}
 	return deg
diff --git a/graph/multi/undirected_test.go b/graph/multi/undirected_test.go
index eba32f8b..a3a1bfc0 100644
--- a/graph/multi/undirected_test.go
+++ b/graph/multi/undirected_test.go
@@ -30,7 +30,7 @@ func TestMaxID(t *testing.T) {
 	delete(nodes, Node(2))
 	n := g.NewNode()
 	g.AddNode(n)
-	if !g.Has(n) {
+	if !g.Has(n.ID()) {
 		t.Error("added node does not exist in graph")
 	}
 	if _, exists := nodes[n]; exists {
diff --git a/graph/multi/weighted_directed.go b/graph/multi/weighted_directed.go
index de96f5c8..c8f86298 100644
--- a/graph/multi/weighted_directed.go
+++ b/graph/multi/weighted_directed.go
@@ -107,13 +107,13 @@ func (g *WeightedDirectedGraph) SetWeightedLine(l graph.WeightedLine) {
 		lid  = l.ID()
 	)
 
-	if !g.Has(from) {
+	if !g.Has(fid) {
 		g.AddNode(from)
 	}
 	if g.from[fid][tid] == nil {
 		g.from[fid][tid] = make(map[int64]graph.WeightedLine)
 	}
-	if !g.Has(to) {
+	if !g.Has(tid) {
 		g.AddNode(to)
 	}
 	if g.to[tid][fid] == nil {
@@ -153,8 +153,8 @@ func (g *WeightedDirectedGraph) Node(id int64) graph.Node {
 }
 
 // Has returns whether the node exists within the graph.
-func (g *WeightedDirectedGraph) Has(n graph.Node) bool {
-	_, ok := g.nodes[n.ID()]
+func (g *WeightedDirectedGraph) Has(id int64) bool {
+	_, ok := g.nodes[id]
 
 	return ok
 }
@@ -213,30 +213,30 @@ func (g *WeightedDirectedGraph) WeightedEdges() []graph.WeightedEdge {
 }
 
 // From returns all nodes in g that can be reached directly from n.
-func (g *WeightedDirectedGraph) From(n graph.Node) []graph.Node {
-	if _, ok := g.from[n.ID()]; !ok {
+func (g *WeightedDirectedGraph) From(id int64) []graph.Node {
+	if _, ok := g.from[id]; !ok {
 		return nil
 	}
 
-	from := make([]graph.Node, len(g.from[n.ID()]))
+	from := make([]graph.Node, len(g.from[id]))
 	i := 0
-	for id := range g.from[n.ID()] {
-		from[i] = g.nodes[id]
+	for vid := range g.from[id] {
+		from[i] = g.nodes[vid]
 		i++
 	}
 	return from
 }
 
 // To returns all nodes in g that can reach directly to n.
-func (g *WeightedDirectedGraph) To(n graph.Node) []graph.Node {
-	if _, ok := g.from[n.ID()]; !ok {
+func (g *WeightedDirectedGraph) To(id int64) []graph.Node {
+	if _, ok := g.from[id]; !ok {
 		return nil
 	}
 
-	to := make([]graph.Node, len(g.to[n.ID()]))
+	to := make([]graph.Node, len(g.to[id]))
 	i := 0
-	for id := range g.to[n.ID()] {
-		to[i] = g.nodes[id]
+	for uid := range g.to[id] {
+		to[i] = g.nodes[uid]
 		i++
 	}
 	return to
@@ -244,9 +244,7 @@ func (g *WeightedDirectedGraph) To(n graph.Node) []graph.Node {
 
 // HasEdgeBetween returns whether an edge exists between nodes x and y without
 // considering direction.
-func (g *WeightedDirectedGraph) HasEdgeBetween(x, y graph.Node) bool {
-	xid := x.ID()
-	yid := y.ID()
+func (g *WeightedDirectedGraph) HasEdgeBetween(xid, yid int64) bool {
 	if _, ok := g.from[xid][yid]; ok {
 		return true
 	}
@@ -255,8 +253,8 @@ func (g *WeightedDirectedGraph) HasEdgeBetween(x, y graph.Node) bool {
 }
 
 // HasEdgeFromTo returns whether an edge exists in the graph from u to v.
-func (g *WeightedDirectedGraph) HasEdgeFromTo(u, v graph.Node) bool {
-	if _, ok := g.from[u.ID()][v.ID()]; !ok {
+func (g *WeightedDirectedGraph) HasEdgeFromTo(uid, vid int64) bool {
+	if _, ok := g.from[uid][vid]; !ok {
 		return false
 	}
 	return true
@@ -265,15 +263,15 @@ func (g *WeightedDirectedGraph) HasEdgeFromTo(u, v graph.Node) bool {
 // Edge returns the edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
 // The returned graph.Edge is a multi.WeightedEdge if an edge exists.
-func (g *WeightedDirectedGraph) Edge(u, v graph.Node) graph.Edge {
-	return g.WeightedEdge(u, v)
+func (g *WeightedDirectedGraph) Edge(uid, vid int64) graph.Edge {
+	return g.WeightedEdge(uid, vid)
 }
 
 // WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
 // The returned graph.WeightedEdge is a multi.WeightedEdge if an edge exists.
-func (g *WeightedDirectedGraph) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
-	lines := g.WeightedLines(u, v)
+func (g *WeightedDirectedGraph) WeightedEdge(uid, vid int64) graph.WeightedEdge {
+	lines := g.WeightedLines(uid, vid)
 	if len(lines) == 0 {
 		return nil
 	}
@@ -282,8 +280,8 @@ func (g *WeightedDirectedGraph) WeightedEdge(u, v graph.Node) graph.WeightedEdge
 
 // Lines returns the lines from u to v if such any such lines exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g *WeightedDirectedGraph) Lines(u, v graph.Node) []graph.Line {
-	edge := g.from[u.ID()][v.ID()]
+func (g *WeightedDirectedGraph) Lines(uid, vid int64) []graph.Line {
+	edge := g.from[uid][vid]
 	if len(edge) == 0 {
 		return nil
 	}
@@ -296,8 +294,8 @@ func (g *WeightedDirectedGraph) Lines(u, v graph.Node) []graph.Line {
 
 // WeightedLines returns the weighted lines from u to v if such any such lines exists
 // and nil otherwise. The node v must be directly reachable from u as defined by the From method.
-func (g *WeightedDirectedGraph) WeightedLines(u, v graph.Node) []graph.WeightedLine {
-	edge := g.from[u.ID()][v.ID()]
+func (g *WeightedDirectedGraph) WeightedLines(uid, vid int64) []graph.WeightedLine {
+	edge := g.from[uid][vid]
 	if len(edge) == 0 {
 		return nil
 	}
@@ -310,21 +308,21 @@ func (g *WeightedDirectedGraph) WeightedLines(u, v graph.Node) []graph.WeightedL
 
 // Weight returns the weight for the lines between x and y summarised by the receiver's
 // EdgeWeightFunc. Weight returns true if an edge exists between x and y, false otherwise.
-func (g *WeightedDirectedGraph) Weight(u, v graph.Node) (w float64, ok bool) {
-	lines := g.WeightedLines(u, v)
+func (g *WeightedDirectedGraph) Weight(uid, vid int64) (w float64, ok bool) {
+	lines := g.WeightedLines(uid, vid)
 	return WeightedEdge{Lines: lines, WeightFunc: g.EdgeWeightFunc}.Weight(), len(lines) != 0
 }
 
 // Degree returns the in+out degree of n in g.
-func (g *WeightedDirectedGraph) Degree(n graph.Node) int {
-	if _, ok := g.nodes[n.ID()]; !ok {
+func (g *WeightedDirectedGraph) Degree(id int64) int {
+	if _, ok := g.nodes[id]; !ok {
 		return 0
 	}
 	var deg int
-	for _, e := range g.from[n.ID()] {
+	for _, e := range g.from[id] {
 		deg += len(e)
 	}
-	for _, e := range g.to[n.ID()] {
+	for _, e := range g.to[id] {
 		deg += len(e)
 	}
 	return deg
diff --git a/graph/multi/weighted_directed_test.go b/graph/multi/weighted_directed_test.go
index 84d18af8..d4e564be 100644
--- a/graph/multi/weighted_directed_test.go
+++ b/graph/multi/weighted_directed_test.go
@@ -22,7 +22,7 @@ var (
 func TestWeightedEdgeOvercounting(t *testing.T) {
 	g := generateDummyWeightedGraph()
 
-	if neigh := g.From(Node(Node(2))); len(neigh) != 2 {
+	if neigh := g.From(int64(2)); len(neigh) != 2 {
 		t.Errorf("Node 2 has incorrect number of neighbors got neighbors %v (count %d), expected 2 neighbors {0,1}", neigh, len(neigh))
 	}
 }
diff --git a/graph/multi/weighted_undirected.go b/graph/multi/weighted_undirected.go
index 3118833e..28546c83 100644
--- a/graph/multi/weighted_undirected.go
+++ b/graph/multi/weighted_undirected.go
@@ -99,13 +99,13 @@ func (g *WeightedUndirectedGraph) SetWeighted(l graph.WeightedLine) {
 		lid  = l.ID()
 	)
 
-	if !g.Has(from) {
+	if !g.Has(fid) {
 		g.AddNode(from)
 	}
 	if g.lines[fid][tid] == nil {
 		g.lines[fid][tid] = make(map[int64]graph.WeightedLine)
 	}
-	if !g.Has(to) {
+	if !g.Has(tid) {
 		g.AddNode(to)
 	}
 	if g.lines[tid][fid] == nil {
@@ -142,8 +142,8 @@ func (g *WeightedUndirectedGraph) Node(id int64) graph.Node {
 }
 
 // Has returns whether the node exists within the graph.
-func (g *WeightedUndirectedGraph) Has(n graph.Node) bool {
-	_, ok := g.nodes[n.ID()]
+func (g *WeightedUndirectedGraph) Has(id int64) bool {
+	_, ok := g.nodes[id]
 	return ok
 }
 
@@ -189,14 +189,14 @@ func (g *WeightedUndirectedGraph) Edges() []graph.Edge {
 }
 
 // From returns all nodes in g that can be reached directly from n.
-func (g *WeightedUndirectedGraph) From(n graph.Node) []graph.Node {
-	if !g.Has(n) {
+func (g *WeightedUndirectedGraph) From(id int64) []graph.Node {
+	if !g.Has(id) {
 		return nil
 	}
 
-	nodes := make([]graph.Node, len(g.lines[n.ID()]))
+	nodes := make([]graph.Node, len(g.lines[id]))
 	i := 0
-	for from := range g.lines[n.ID()] {
+	for from := range g.lines[id] {
 		nodes[i] = g.nodes[from]
 		i++
 	}
@@ -204,20 +204,20 @@ func (g *WeightedUndirectedGraph) From(n graph.Node) []graph.Node {
 }
 
 // HasEdgeBetween returns whether an edge exists between nodes x and y.
-func (g *WeightedUndirectedGraph) HasEdgeBetween(x, y graph.Node) bool {
-	_, ok := g.lines[x.ID()][y.ID()]
+func (g *WeightedUndirectedGraph) HasEdgeBetween(xid, yid int64) bool {
+	_, ok := g.lines[xid][yid]
 	return ok
 }
 
 // Lines returns the lines from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g *WeightedUndirectedGraph) Lines(u, v graph.Node) []graph.Line {
-	return g.LinesBetween(u, v)
+func (g *WeightedUndirectedGraph) Lines(uid, vid int64) []graph.Line {
+	return g.LinesBetween(uid, vid)
 }
 
 // LinesBetween returns the lines between nodes x and y.
-func (g *WeightedUndirectedGraph) LinesBetween(x, y graph.Node) []graph.Line {
-	edge := g.lines[x.ID()][y.ID()]
+func (g *WeightedUndirectedGraph) LinesBetween(xid, yid int64) []graph.Line {
+	edge := g.lines[xid][yid]
 	if len(edge) == 0 {
 		return nil
 	}
@@ -237,20 +237,20 @@ func (g *WeightedUndirectedGraph) LinesBetween(x, y graph.Node) []graph.Line {
 // Edge returns the edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
 // The returned graph.Edge is a multi.WeightedEdge if an edge exists.
-func (g *WeightedUndirectedGraph) Edge(u, v graph.Node) graph.Edge {
-	return g.WeightedEdge(u, v)
+func (g *WeightedUndirectedGraph) Edge(uid, vid int64) graph.Edge {
+	return g.WeightedEdge(uid, vid)
 }
 
 // EdgeBetween returns the edge between nodes x and y.
-func (g *WeightedUndirectedGraph) EdgeBetween(x, y graph.Node) graph.Edge {
-	return g.WeightedEdge(x, y)
+func (g *WeightedUndirectedGraph) EdgeBetween(xid, yid int64) graph.Edge {
+	return g.WeightedEdge(xid, yid)
 }
 
 // WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
 // The returned graph.WeightedEdge is a multi.WeightedEdge if an edge exists.
-func (g *WeightedUndirectedGraph) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
-	lines := g.WeightedLines(u, v)
+func (g *WeightedUndirectedGraph) WeightedEdge(uid, vid int64) graph.WeightedEdge {
+	lines := g.WeightedLines(uid, vid)
 	if len(lines) == 0 {
 		return nil
 	}
@@ -258,19 +258,19 @@ func (g *WeightedUndirectedGraph) WeightedEdge(u, v graph.Node) graph.WeightedEd
 }
 
 // WeightedEdgeBetween returns the weighted edge between nodes x and y.
-func (g *WeightedUndirectedGraph) WeightedEdgeBetween(x, y graph.Node) graph.WeightedEdge {
-	return g.WeightedEdge(x, y)
+func (g *WeightedUndirectedGraph) WeightedEdgeBetween(xid, yid int64) graph.WeightedEdge {
+	return g.WeightedEdge(xid, yid)
 }
 
 // WeightedLines returns the lines from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g *WeightedUndirectedGraph) WeightedLines(u, v graph.Node) []graph.WeightedLine {
-	return g.WeightedLinesBetween(u, v)
+func (g *WeightedUndirectedGraph) WeightedLines(uid, vid int64) []graph.WeightedLine {
+	return g.WeightedLinesBetween(uid, vid)
 }
 
 // WeightedLinesBetween returns the lines between nodes x and y.
-func (g *WeightedUndirectedGraph) WeightedLinesBetween(x, y graph.Node) []graph.WeightedLine {
-	edge := g.lines[x.ID()][y.ID()]
+func (g *WeightedUndirectedGraph) WeightedLinesBetween(xid, yid int64) []graph.WeightedLine {
+	edge := g.lines[xid][yid]
 	if len(edge) == 0 {
 		return nil
 	}
@@ -289,18 +289,18 @@ func (g *WeightedUndirectedGraph) WeightedLinesBetween(x, y graph.Node) []graph.
 
 // Weight returns the weight for the lines between x and y summarised by the receiver's
 // EdgeWeightFunc. Weight returns true if an edge exists between x and y, false otherwise.
-func (g *WeightedUndirectedGraph) Weight(x, y graph.Node) (w float64, ok bool) {
-	lines := g.WeightedLines(x, y)
+func (g *WeightedUndirectedGraph) Weight(xid, yid int64) (w float64, ok bool) {
+	lines := g.WeightedLines(xid, yid)
 	return WeightedEdge{Lines: lines, WeightFunc: g.EdgeWeightFunc}.Weight(), len(lines) != 0
 }
 
 // Degree returns the degree of n in g.
-func (g *WeightedUndirectedGraph) Degree(n graph.Node) int {
-	if _, ok := g.nodes[n.ID()]; !ok {
+func (g *WeightedUndirectedGraph) Degree(id int64) int {
+	if _, ok := g.nodes[id]; !ok {
 		return 0
 	}
 	var deg int
-	for _, e := range g.lines[n.ID()] {
+	for _, e := range g.lines[id] {
 		deg += len(e)
 	}
 	return deg
diff --git a/graph/multi/weighted_undirected_test.go b/graph/multi/weighted_undirected_test.go
index dc32a45c..df190902 100644
--- a/graph/multi/weighted_undirected_test.go
+++ b/graph/multi/weighted_undirected_test.go
@@ -23,7 +23,7 @@ func TestWeightedMaxID(t *testing.T) {
 	delete(nodes, Node(2))
 	n := g.NewNode()
 	g.AddNode(n)
-	if !g.Has(n) {
+	if !g.Has(n.ID()) {
 		t.Error("added node does not exist in graph")
 	}
 	if _, exists := nodes[n]; exists {
diff --git a/graph/multigraph.go b/graph/multigraph.go
index 67adaf59..249f9294 100644
--- a/graph/multigraph.go
+++ b/graph/multigraph.go
@@ -19,43 +19,46 @@ type WeightedLine interface {
 
 // Multigraph is a generalized multigraph.
 type Multigraph interface {
-	// Has returns whether the node exists within the multigraph.
-	Has(Node) bool
+	// Has returns whether the node with the given ID exists
+	// within the multigraph.
+	Has(id int64) bool
 
 	// Nodes returns all the nodes in the multigraph.
 	Nodes() []Node
 
 	// From returns all nodes that can be reached directly
-	// from the given node.
-	From(Node) []Node
+	// from the node with the given ID.
+	From(id int64) []Node
 
 	// HasEdgeBetween returns whether an edge exists between
-	// nodes x and y without considering direction.
-	HasEdgeBetween(x, y Node) bool
+	// nodes with IDs xid and yid without considering direction.
+	HasEdgeBetween(xid, yid int64) bool
 
-	// Lines returns the lines from u to v if any such lines
-	// exist and nil otherwise. The node v must be directly
-	// reachable from u as defined by the From method.
-	Lines(u, v Node) []Line
+	// Lines returns the lines from u to v, with IDs uid and
+	// vid, if any such lines exist and nil otherwise. The
+	// node v must be directly reachable from u as defined by
+	// the From method.
+	Lines(uid, vid int64) []Line
 }
 
 // WeightedMultigraph is a weighted multigraph.
 type WeightedMultigraph interface {
 	Multigraph
 
-	// WeightedLines returns the weighted lines from u to v if
-	// any such lines exist and nil otherwise. The node v must
-	// be directly reachable from u as defined by the
-	// From method.
-	WeightedLines(u, v Node) []WeightedLine
+	// WeightedLines returns the weighted lines from u to v
+	// with IDs uid and vid if any such lines exist and nil
+	// otherwise. The node v must be directly reachable
+	// from u as defined by the From method.
+	WeightedLines(uid, vid int64) []WeightedLine
 }
 
 // UndirectedMultigraph is an undirected multigraph.
 type UndirectedMultigraph interface {
 	Multigraph
 
-	// LinesBetween returns the lines between nodes x and y.
-	LinesBetween(x, y Node) []Line
+	// LinesBetween returns the lines between nodes x and y
+	// with IDs xid and yid.
+	LinesBetween(xid, yid int64) []Line
 }
 
 // WeightedUndirectedMultigraph is a weighted undirected multigraph.
@@ -63,8 +66,8 @@ type WeightedUndirectedMultigraph interface {
 	WeightedMultigraph
 
 	// WeightedLinesBetween returns the lines between nodes
-	// x and y.
-	WeightedLinesBetween(x, y Node) []WeightedLine
+	// x and y with IDs xid and yid.
+	WeightedLinesBetween(xid, yid int64) []WeightedLine
 }
 
 // DirectedMultigraph is a directed multigraph.
@@ -72,12 +75,13 @@ type DirectedMultigraph interface {
 	Multigraph
 
 	// HasEdgeFromTo returns whether an edge exists
-	// in the multigraph from u to v.
-	HasEdgeFromTo(u, v Node) bool
+	// in the multigraph from u to v with IDs uid
+	// and vid.
+	HasEdgeFromTo(uid, vid int64) bool
 
 	// To returns all nodes that can reach directly
-	// to the given node.
-	To(Node) []Node
+	// to the node with the given ID.
+	To(id int64) []Node
 }
 
 // WeightedDirectedMultigraph is a weighted directed multigraph.
@@ -85,12 +89,13 @@ type WeightedDirectedMultigraph interface {
 	WeightedMultigraph
 
 	// HasEdgeFromTo returns whether an edge exists
-	// in the multigraph from u to v.
-	HasEdgeFromTo(u, v Node) bool
+	// in the multigraph from u to v with IDs uid
+	// and vid.
+	HasEdgeFromTo(uid, vid int64) bool
 
 	// To returns all nodes that can reach directly
-	// to the given node.
-	To(Node) []Node
+	// to the node with the given ID.
+	To(id int64) []Node
 }
 
 // LineAdder is an interface for adding lines to a multigraph.
diff --git a/graph/network/betweenness.go b/graph/network/betweenness.go
index abb3face..70b816c9 100644
--- a/graph/network/betweenness.go
+++ b/graph/network/betweenness.go
@@ -115,17 +115,19 @@ func brandes(g graph.Graph, accumulate func(s graph.Node, stack linear.NodeStack
 		queue.Enqueue(s)
 		for queue.Len() != 0 {
 			v := queue.Dequeue()
+			vid := v.ID()
 			stack.Push(v)
-			for _, w := range g.From(v) {
+			for _, w := range g.From(vid) {
+				wid := w.ID()
 				// w found for the first time?
-				if d[w.ID()] < 0 {
+				if d[wid] < 0 {
 					queue.Enqueue(w)
-					d[w.ID()] = d[v.ID()] + 1
+					d[wid] = d[vid] + 1
 				}
 				// shortest path to w via v?
-				if d[w.ID()] == d[v.ID()]+1 {
-					sigma[w.ID()] += sigma[v.ID()]
-					p[w.ID()] = append(p[w.ID()], v)
+				if d[wid] == d[vid]+1 {
+					sigma[wid] += sigma[vid]
+					p[wid] = append(p[wid], v)
 				}
 			}
 		}
@@ -151,18 +153,20 @@ func BetweennessWeighted(g graph.Weighted, p path.AllShortest) map[int64]float64
 
 	nodes := g.Nodes()
 	for i, s := range nodes {
+		sid := s.ID()
 		for j, t := range nodes {
 			if i == j {
 				continue
 			}
-			d := p.Weight(s, t)
+			tid := t.ID()
+			d := p.Weight(sid, tid)
 			if math.IsInf(d, 0) {
 				continue
 			}
 
 			// If we have a unique path, don't do the
 			// extra work needed to get all paths.
-			path, _, unique := p.Between(s, t)
+			path, _, unique := p.Between(sid, tid)
 			if unique {
 				for _, v := range path[1 : len(path)-1] {
 					// For undirected graphs we double count
@@ -174,7 +178,7 @@ func BetweennessWeighted(g graph.Weighted, p path.AllShortest) map[int64]float64
 			}
 
 			// Otherwise iterate over all paths.
-			paths, _ := p.AllBetween(s, t)
+			paths, _ := p.AllBetween(sid, tid)
 			stFrac := 1 / float64(len(paths))
 			for _, path := range paths {
 				for _, v := range path[1 : len(path)-1] {
@@ -203,18 +207,20 @@ func EdgeBetweennessWeighted(g graph.Weighted, p path.AllShortest) map[[2]int64]
 	_, isUndirected := g.(graph.Undirected)
 	nodes := g.Nodes()
 	for i, s := range nodes {
+		sid := s.ID()
 		for j, t := range nodes {
 			if i == j {
 				continue
 			}
-			d := p.Weight(s, t)
+			tid := t.ID()
+			d := p.Weight(sid, tid)
 			if math.IsInf(d, 0) {
 				continue
 			}
 
 			// If we have a unique path, don't do the
 			// extra work needed to get all paths.
-			path, _, unique := p.Between(s, t)
+			path, _, unique := p.Between(sid, tid)
 			if unique {
 				for k, v := range path[1:] {
 					// For undirected graphs we double count
@@ -231,7 +237,7 @@ func EdgeBetweennessWeighted(g graph.Weighted, p path.AllShortest) map[[2]int64]
 			}
 
 			// Otherwise iterate over all paths.
-			paths, _ := p.AllBetween(s, t)
+			paths, _ := p.AllBetween(sid, tid)
 			stFrac := 1 / float64(len(paths))
 			for _, path := range paths {
 				for k, v := range path[1:] {
diff --git a/graph/network/betweenness_test.go b/graph/network/betweenness_test.go
index bcea1461..75864733 100644
--- a/graph/network/betweenness_test.go
+++ b/graph/network/betweenness_test.go
@@ -179,7 +179,7 @@ func TestBetweenness(t *testing.T) {
 		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -208,7 +208,7 @@ func TestEdgeBetweenness(t *testing.T) {
 		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -240,7 +240,7 @@ func TestBetweennessWeighted(t *testing.T) {
 		g := simple.NewWeightedUndirectedGraph(0, math.Inf(1))
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -276,7 +276,7 @@ func TestEdgeBetweennessWeighted(t *testing.T) {
 		g := simple.NewWeightedUndirectedGraph(0, math.Inf(1))
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
diff --git a/graph/network/diffusion.go b/graph/network/diffusion.go
index 11b5832f..087c4b8a 100644
--- a/graph/network/diffusion.go
+++ b/graph/network/diffusion.go
@@ -122,9 +122,9 @@ func NewLaplacian(g graph.Undirected) Laplacian {
 
 	l := mat.NewSymDense(len(nodes), nil)
 	for j, u := range nodes {
-		to := g.From(u)
-		l.SetSym(j, j, float64(len(to)))
 		uid := u.ID()
+		to := g.From(uid)
+		l.SetSym(j, j, float64(len(to)))
 		for _, v := range to {
 			vid := v.ID()
 			if uid == vid {
@@ -155,12 +155,12 @@ func NewSymNormLaplacian(g graph.Undirected) Laplacian {
 
 	l := mat.NewSymDense(len(nodes), nil)
 	for j, u := range nodes {
-		to := g.From(u)
+		uid := u.ID()
+		to := g.From(uid)
 		if len(to) == 0 {
 			continue
 		}
 		l.SetSym(j, j, 1)
-		uid := u.ID()
 		squdeg := math.Sqrt(float64(len(to)))
 		for _, v := range to {
 			vid := v.ID()
@@ -168,7 +168,7 @@ func NewSymNormLaplacian(g graph.Undirected) Laplacian {
 				panic("network: self edge in graph")
 			}
 			if uid < vid {
-				l.SetSym(indexOf[vid], j, -1/(squdeg*math.Sqrt(float64(len(g.From(v))))))
+				l.SetSym(indexOf[vid], j, -1/(squdeg*math.Sqrt(float64(len(g.From(vid))))))
 			}
 		}
 	}
@@ -193,7 +193,7 @@ func NewRandomWalkLaplacian(g graph.Graph, damp float64) Laplacian {
 	l := mat.NewDense(len(nodes), len(nodes), nil)
 	for j, u := range nodes {
 		uid := u.ID()
-		to := g.From(u)
+		to := g.From(uid)
 		if len(to) == 0 {
 			continue
 		}
diff --git a/graph/network/diffusion_test.go b/graph/network/diffusion_test.go
index b5bc993f..e8b2f8e3 100644
--- a/graph/network/diffusion_test.go
+++ b/graph/network/diffusion_test.go
@@ -152,7 +152,7 @@ func TestDiffuse(t *testing.T) {
 		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -278,7 +278,7 @@ func TestRandomWalkLaplacian(t *testing.T) {
 		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -466,7 +466,7 @@ func TestDiffuseToEquilibrium(t *testing.T) {
 		g := test.builder
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
diff --git a/graph/network/distance.go b/graph/network/distance.go
index ce37ddca..a97695c5 100644
--- a/graph/network/distance.go
+++ b/graph/network/distance.go
@@ -22,12 +22,14 @@ func Closeness(g graph.Graph, p path.AllShortest) map[int64]float64 {
 	nodes := g.Nodes()
 	c := make(map[int64]float64, len(nodes))
 	for _, u := range nodes {
+		uid := u.ID()
 		var sum float64
 		for _, v := range nodes {
+			vid := v.ID()
 			// The ordering here is not relevant for
 			// undirected graphs, but we make sure we
 			// are counting incoming paths.
-			d := p.Weight(v, u)
+			d := p.Weight(vid, uid)
 			if math.IsInf(d, 0) {
 				continue
 			}
@@ -49,12 +51,14 @@ func Farness(g graph.Graph, p path.AllShortest) map[int64]float64 {
 	nodes := g.Nodes()
 	f := make(map[int64]float64, len(nodes))
 	for _, u := range nodes {
+		uid := u.ID()
 		var sum float64
 		for _, v := range nodes {
+			vid := v.ID()
 			// The ordering here is not relevant for
 			// undirected graphs, but we make sure we
 			// are counting incoming paths.
-			d := p.Weight(v, u)
+			d := p.Weight(vid, uid)
 			if math.IsInf(d, 0) {
 				continue
 			}
@@ -76,12 +80,14 @@ func Harmonic(g graph.Graph, p path.AllShortest) map[int64]float64 {
 	nodes := g.Nodes()
 	h := make(map[int64]float64, len(nodes))
 	for i, u := range nodes {
+		uid := u.ID()
 		var sum float64
 		for j, v := range nodes {
+			vid := v.ID()
 			// The ordering here is not relevant for
 			// undirected graphs, but we make sure we
 			// are counting incoming paths.
-			d := p.Weight(v, u)
+			d := p.Weight(vid, uid)
 			if math.IsInf(d, 0) {
 				continue
 			}
@@ -105,12 +111,14 @@ func Residual(g graph.Graph, p path.AllShortest) map[int64]float64 {
 	nodes := g.Nodes()
 	r := make(map[int64]float64, len(nodes))
 	for i, u := range nodes {
+		uid := u.ID()
 		var sum float64
 		for j, v := range nodes {
+			vid := v.ID()
 			// The ordering here is not relevant for
 			// undirected graphs, but we make sure we
 			// are counting incoming paths.
-			d := p.Weight(v, u)
+			d := p.Weight(vid, uid)
 			if math.IsInf(d, 0) {
 				continue
 			}
diff --git a/graph/network/distance_test.go b/graph/network/distance_test.go
index f2e8ec2c..02bb724d 100644
--- a/graph/network/distance_test.go
+++ b/graph/network/distance_test.go
@@ -146,7 +146,7 @@ func TestDistanceCentralityUndirected(t *testing.T) {
 		g := simple.NewWeightedUndirectedGraph(0, math.Inf(1))
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -336,7 +336,7 @@ func TestDistanceCentralityDirected(t *testing.T) {
 		g := simple.NewWeightedDirectedGraph(0, math.Inf(1))
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
diff --git a/graph/network/hits.go b/graph/network/hits.go
index 763a32ee..fe8d05ca 100644
--- a/graph/network/hits.go
+++ b/graph/network/hits.go
@@ -32,10 +32,11 @@ func HITS(g graph.Directed, tol float64) map[int64]HubAuthority {
 	nodesLinkingTo := make([][]int, len(nodes))
 	nodesLinkedFrom := make([][]int, len(nodes))
 	for i, n := range nodes {
-		for _, u := range g.To(n) {
+		id := n.ID()
+		for _, u := range g.To(id) {
 			nodesLinkingTo[i] = append(nodesLinkingTo[i], indexOf[u.ID()])
 		}
-		for _, v := range g.From(n) {
+		for _, v := range g.From(id) {
 			nodesLinkedFrom[i] = append(nodesLinkedFrom[i], indexOf[v.ID()])
 		}
 	}
diff --git a/graph/network/hits_test.go b/graph/network/hits_test.go
index a2ec30c7..af1ea087 100644
--- a/graph/network/hits_test.go
+++ b/graph/network/hits_test.go
@@ -46,7 +46,7 @@ func TestHITS(t *testing.T) {
 		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
diff --git a/graph/network/page.go b/graph/network/page.go
index 980ff6e7..7d7ee0a5 100644
--- a/graph/network/page.go
+++ b/graph/network/page.go
@@ -35,7 +35,7 @@ func PageRank(g graph.Directed, damp, tol float64) map[int64]float64 {
 	m := mat.NewDense(len(nodes), len(nodes), nil)
 	dangling := damp / float64(len(nodes))
 	for j, u := range nodes {
-		to := g.From(u)
+		to := g.From(u.ID())
 		f := damp / float64(len(to))
 		for _, v := range to {
 			m.Set(indexOf[v.ID()], j, f)
@@ -109,7 +109,7 @@ func PageRankSparse(g graph.Directed, damp, tol float64) map[int64]float64 {
 	var dangling compressedRow
 	df := damp / float64(len(nodes))
 	for j, u := range nodes {
-		to := g.From(u)
+		to := g.From(u.ID())
 		f := damp / float64(len(to))
 		for _, v := range to {
 			m.addTo(indexOf[v.ID()], j, f)
diff --git a/graph/network/page_test.go b/graph/network/page_test.go
index 3d37fd8e..ac53148e 100644
--- a/graph/network/page_test.go
+++ b/graph/network/page_test.go
@@ -84,7 +84,7 @@ func TestPageRank(t *testing.T) {
 		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -108,7 +108,7 @@ func TestPageRankSparse(t *testing.T) {
 		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
diff --git a/graph/path/a_star.go b/graph/path/a_star.go
index b4e2609e..a91da5f6 100644
--- a/graph/path/a_star.go
+++ b/graph/path/a_star.go
@@ -24,7 +24,7 @@ import (
 // falling back to NullHeuristic otherwise. If the graph does not implement graph.Weighter,
 // UniformCost is used. AStar will panic if g has an A*-reachable negative edge weight.
 func AStar(s, t graph.Node, g graph.Graph, h Heuristic) (path Shortest, expanded int) {
-	if !g.Has(s) || !g.Has(t) {
+	if !g.Has(s.ID()) || !g.Has(t.ID()) {
 		return Shortest{from: s}, 0
 	}
 	var weight Weighting
@@ -59,14 +59,14 @@ func AStar(s, t graph.Node, g graph.Graph, h Heuristic) (path Shortest, expanded
 		}
 
 		visited.Add(uid)
-		for _, v := range g.From(u.node) {
+		for _, v := range g.From(u.node.ID()) {
 			vid := v.ID()
 			if visited.Has(vid) {
 				continue
 			}
 			j := path.indexOf[vid]
 
-			w, ok := weight(u.node, v)
+			w, ok := weight(u.node.ID(), vid)
 			if !ok {
 				panic("A*: unexpected invalid weight")
 			}
diff --git a/graph/path/a_star_test.go b/graph/path/a_star_test.go
index 88e2ea47..e4bd3c57 100644
--- a/graph/path/a_star_test.go
+++ b/graph/path/a_star_test.go
@@ -129,7 +129,7 @@ func TestAStar(t *testing.T) {
 	for _, test := range aStarTests {
 		pt, _ := AStar(simple.Node(test.s), simple.Node(test.t), test.g, test.heuristic)
 
-		p, cost := pt.To(simple.Node(test.t))
+		p, cost := pt.To(test.t)
 
 		if !topo.IsPathIn(test.g, p) {
 			t.Errorf("got path that is not path in input graph for %q", test.name)
@@ -139,7 +139,7 @@ func TestAStar(t *testing.T) {
 		if !ok {
 			t.Fatalf("unexpected negative cycle in %q", test.name)
 		}
-		if want := bfp.WeightTo(simple.Node(test.t)); cost != want {
+		if want := bfp.WeightTo(test.t); cost != want {
 			t.Errorf("unexpected cost for %q: got:%v want:%v", test.name, cost, want)
 		}
 
@@ -196,8 +196,8 @@ func TestExhaustiveAStar(t *testing.T) {
 	for _, start := range g.Nodes() {
 		for _, goal := range g.Nodes() {
 			pt, _ := AStar(start, goal, g, heuristic)
-			gotPath, gotWeight := pt.To(goal)
-			wantPath, wantWeight, _ := ps.Between(start, goal)
+			gotPath, gotWeight := pt.To(goal.ID())
+			wantPath, wantWeight, _ := ps.Between(start.ID(), goal.ID())
 			if gotWeight != wantWeight {
 				t.Errorf("unexpected path weight from %v to %v result: got:%f want:%f",
 					start, goal, gotWeight, wantWeight)
@@ -231,7 +231,7 @@ func isMonotonic(g UndirectedWeightLister, h Heuristic) (ok bool, at graph.Edge,
 		for _, edge := range g.WeightedEdges() {
 			from := edge.From()
 			to := edge.To()
-			w, ok := g.Weight(from, to)
+			w, ok := g.Weight(from.ID(), to.ID())
 			if !ok {
 				panic("A*: unexpected invalid weight")
 			}
@@ -275,12 +275,12 @@ func TestAStarNullHeuristic(t *testing.T) {
 			t.Fatalf("%q: unexpected from node ID: got:%d want:%d", test.Name, pt.From().ID(), test.Query.From().ID())
 		}
 
-		p, weight := pt.To(test.Query.To())
+		p, weight := pt.To(test.Query.To().ID())
 		if weight != test.Weight {
 			t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
 				test.Name, weight, test.Weight)
 		}
-		if weight := pt.WeightTo(test.Query.To()); weight != test.Weight {
+		if weight := pt.WeightTo(test.Query.To().ID()); weight != test.Weight {
 			t.Errorf("%q: unexpected weight from Weight: got:%f want:%f",
 				test.Name, weight, test.Weight)
 		}
@@ -301,7 +301,7 @@ func TestAStarNullHeuristic(t *testing.T) {
 				test.Name, p, test.WantPaths)
 		}
 
-		np, weight := pt.To(test.NoPathFor.To())
+		np, weight := pt.To(test.NoPathFor.To().ID())
 		if pt.From().ID() == test.NoPathFor.From().ID() && (np != nil || !math.IsInf(weight, 1)) {
 			t.Errorf("%q: unexpected path:\ngot: path=%v weight=%f\nwant:path=<nil> weight=+Inf",
 				test.Name, np, weight)
diff --git a/graph/path/bellman_ford_moore.go b/graph/path/bellman_ford_moore.go
index 03e37428..9786175b 100644
--- a/graph/path/bellman_ford_moore.go
+++ b/graph/path/bellman_ford_moore.go
@@ -12,7 +12,7 @@ import "gonum.org/v1/gonum/graph"
 //
 // The time complexity of BellmanFordFrom is O(|V|.|E|).
 func BellmanFordFrom(u graph.Node, g graph.Graph) (path Shortest, ok bool) {
-	if !g.Has(u) {
+	if !g.Has(u.ID()) {
 		return Shortest{from: u}, true
 	}
 	var weight Weighting
@@ -32,9 +32,11 @@ func BellmanFordFrom(u graph.Node, g graph.Graph) (path Shortest, ok bool) {
 	for i := 1; i < len(nodes); i++ {
 		changed := false
 		for j, u := range nodes {
-			for _, v := range g.From(u) {
-				k := path.indexOf[v.ID()]
-				w, ok := weight(u, v)
+			uid := u.ID()
+			for _, v := range g.From(uid) {
+				vid := v.ID()
+				k := path.indexOf[vid]
+				w, ok := weight(uid, vid)
 				if !ok {
 					panic("bellman-ford: unexpected invalid weight")
 				}
@@ -51,9 +53,11 @@ func BellmanFordFrom(u graph.Node, g graph.Graph) (path Shortest, ok bool) {
 	}
 
 	for j, u := range nodes {
-		for _, v := range g.From(u) {
-			k := path.indexOf[v.ID()]
-			w, ok := weight(u, v)
+		uid := u.ID()
+		for _, v := range g.From(uid) {
+			vid := v.ID()
+			k := path.indexOf[vid]
+			w, ok := weight(uid, vid)
 			if !ok {
 				panic("bellman-ford: unexpected invalid weight")
 			}
diff --git a/graph/path/bellman_ford_moore_test.go b/graph/path/bellman_ford_moore_test.go
index c9416448..2d4b9c2b 100644
--- a/graph/path/bellman_ford_moore_test.go
+++ b/graph/path/bellman_ford_moore_test.go
@@ -35,12 +35,12 @@ func TestBellmanFordFrom(t *testing.T) {
 			t.Fatalf("%q: unexpected from node ID: got:%d want:%d", test.Name, pt.From().ID(), test.Query.From().ID())
 		}
 
-		p, weight := pt.To(test.Query.To())
+		p, weight := pt.To(test.Query.To().ID())
 		if weight != test.Weight {
 			t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
 				test.Name, weight, test.Weight)
 		}
-		if weight := pt.WeightTo(test.Query.To()); weight != test.Weight {
+		if weight := pt.WeightTo(test.Query.To().ID()); weight != test.Weight {
 			t.Errorf("%q: unexpected weight from Weight: got:%f want:%f",
 				test.Name, weight, test.Weight)
 		}
@@ -61,7 +61,7 @@ func TestBellmanFordFrom(t *testing.T) {
 				test.Name, p, test.WantPaths)
 		}
 
-		np, weight := pt.To(test.NoPathFor.To())
+		np, weight := pt.To(test.NoPathFor.To().ID())
 		if pt.From().ID() == test.NoPathFor.From().ID() && (np != nil || !math.IsInf(weight, 1)) {
 			t.Errorf("%q: unexpected path:\ngot: path=%v weight=%f\nwant:path=<nil> weight=+Inf",
 				test.Name, np, weight)
diff --git a/graph/path/control_flow_bench_test.go b/graph/path/control_flow_bench_test.go
index cdb50ef5..d2506aef 100644
--- a/graph/path/control_flow_bench_test.go
+++ b/graph/path/control_flow_bench_test.go
@@ -201,7 +201,7 @@ func BenchmarkRandomGraphDominators(b *testing.B) {
 				if v == nil {
 					v = unordered[ui][rnd.Intn(len(unordered[ui]))]
 				}
-				if !g.HasEdgeFromTo(u, v) {
+				if !g.HasEdgeFromTo(u.ID(), v.ID()) {
 					g.SetEdge(g.NewEdge(u, v))
 				}
 			}
@@ -253,16 +253,16 @@ type undirected struct {
 	*simple.DirectedGraph
 }
 
-func (g undirected) From(n graph.Node) []graph.Node {
-	return append(g.DirectedGraph.From(n), g.DirectedGraph.To(n)...)
+func (g undirected) From(id int64) []graph.Node {
+	return append(g.DirectedGraph.From(id), g.DirectedGraph.To(id)...)
 }
 
-func (g undirected) HasEdgeBetween(x, y graph.Node) bool {
-	return g.DirectedGraph.HasEdgeFromTo(x, y)
+func (g undirected) HasEdgeBetween(xid, yid int64) bool {
+	return g.DirectedGraph.HasEdgeFromTo(xid, yid)
 }
 
-func (g undirected) EdgeBetween(x, y graph.Node) graph.Edge {
-	return g.DirectedGraph.Edge(x, y)
+func (g undirected) EdgeBetween(xid, yid int64) graph.Edge {
+	return g.DirectedGraph.Edge(xid, yid)
 }
 
 func (g undirected) SetEdge(e graph.Edge) {
diff --git a/graph/path/control_flow_lt.go b/graph/path/control_flow_lt.go
index 0062c1a2..7bb66980 100644
--- a/graph/path/control_flow_lt.go
+++ b/graph/path/control_flow_lt.go
@@ -140,7 +140,7 @@ func (lt *lengauerTarjan) dfs(g graph.Directed, v graph.Node) {
 	ltv.label = ltv
 	lt.nodes = append(lt.nodes, ltv)
 
-	for _, w := range g.From(v) {
+	for _, w := range g.From(v.ID()) {
 		wid := w.ID()
 
 		idx, ok := lt.indexOf[wid]
diff --git a/graph/path/control_flow_slt.go b/graph/path/control_flow_slt.go
index 2b6a995f..379b92d9 100644
--- a/graph/path/control_flow_slt.go
+++ b/graph/path/control_flow_slt.go
@@ -162,7 +162,7 @@ func (lt *sLengauerTarjan) dfs(g graph.Directed, v graph.Node) {
 	ltv.label = ltv
 	lt.nodes = append(lt.nodes, ltv)
 
-	for _, w := range g.From(v) {
+	for _, w := range g.From(v.ID()) {
 		wid := w.ID()
 
 		idx, ok := lt.indexOf[wid]
diff --git a/graph/path/dijkstra.go b/graph/path/dijkstra.go
index bdbc49bd..6a8a37eb 100644
--- a/graph/path/dijkstra.go
+++ b/graph/path/dijkstra.go
@@ -16,7 +16,7 @@ import (
 //
 // The time complexity of DijkstrFrom is O(|E|.log|V|).
 func DijkstraFrom(u graph.Node, g graph.Graph) Shortest {
-	if !g.Has(u) {
+	if !g.Has(u.ID()) {
 		return Shortest{from: u}
 	}
 	var weight Weighting
@@ -46,9 +46,11 @@ func DijkstraFrom(u graph.Node, g graph.Graph) Shortest {
 		if mid.dist > path.dist[k] {
 			continue
 		}
-		for _, v := range g.From(mid.node) {
-			j := path.indexOf[v.ID()]
-			w, ok := weight(mid.node, v)
+		mnid := mid.node.ID()
+		for _, v := range g.From(mnid) {
+			vid := v.ID()
+			j := path.indexOf[vid]
+			w, ok := weight(mnid, vid)
 			if !ok {
 				panic("dijkstra: unexpected invalid weight")
 			}
@@ -106,9 +108,11 @@ func dijkstraAllPaths(g graph.Graph, paths AllShortest) {
 			if mid.dist < paths.dist.At(i, k) {
 				paths.dist.Set(i, k, mid.dist)
 			}
-			for _, v := range g.From(mid.node) {
-				j := paths.indexOf[v.ID()]
-				w, ok := weight(mid.node, v)
+			mnid := mid.node.ID()
+			for _, v := range g.From(mnid) {
+				vid := v.ID()
+				j := paths.indexOf[vid]
+				w, ok := weight(mnid, vid)
 				if !ok {
 					panic("dijkstra: unexpected invalid weight")
 				}
diff --git a/graph/path/dijkstra_test.go b/graph/path/dijkstra_test.go
index 54a2d23c..fe6450e2 100644
--- a/graph/path/dijkstra_test.go
+++ b/graph/path/dijkstra_test.go
@@ -47,12 +47,12 @@ func TestDijkstraFrom(t *testing.T) {
 			t.Fatalf("%q: unexpected from node ID: got:%d want:%d", test.Name, pt.From().ID(), test.Query.From().ID())
 		}
 
-		p, weight := pt.To(test.Query.To())
+		p, weight := pt.To(test.Query.To().ID())
 		if weight != test.Weight {
 			t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
 				test.Name, weight, test.Weight)
 		}
-		if weight := pt.WeightTo(test.Query.To()); weight != test.Weight {
+		if weight := pt.WeightTo(test.Query.To().ID()); weight != test.Weight {
 			t.Errorf("%q: unexpected weight from Weight: got:%f want:%f",
 				test.Name, weight, test.Weight)
 		}
@@ -73,7 +73,7 @@ func TestDijkstraFrom(t *testing.T) {
 				test.Name, p, test.WantPaths)
 		}
 
-		np, weight := pt.To(test.NoPathFor.To())
+		np, weight := pt.To(test.NoPathFor.To().ID())
 		if pt.From().ID() == test.NoPathFor.From().ID() && (np != nil || !math.IsInf(weight, 1)) {
 			t.Errorf("%q: unexpected path:\ngot: path=%v weight=%f\nwant:path=<nil> weight=+Inf",
 				test.Name, np, weight)
@@ -111,12 +111,12 @@ func TestDijkstraAllPaths(t *testing.T) {
 
 		// Check all random paths returned are OK.
 		for i := 0; i < 10; i++ {
-			p, weight, unique := pt.Between(test.Query.From(), test.Query.To())
+			p, weight, unique := pt.Between(test.Query.From().ID(), test.Query.To().ID())
 			if weight != test.Weight {
 				t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
 					test.Name, weight, test.Weight)
 			}
-			if weight := pt.Weight(test.Query.From(), test.Query.To()); weight != test.Weight {
+			if weight := pt.Weight(test.Query.From().ID(), test.Query.To().ID()); weight != test.Weight {
 				t.Errorf("%q: unexpected weight from Weight: got:%f want:%f",
 					test.Name, weight, test.Weight)
 			}
@@ -142,13 +142,13 @@ func TestDijkstraAllPaths(t *testing.T) {
 			}
 		}
 
-		np, weight, unique := pt.Between(test.NoPathFor.From(), test.NoPathFor.To())
+		np, weight, unique := pt.Between(test.NoPathFor.From().ID(), test.NoPathFor.To().ID())
 		if np != nil || !math.IsInf(weight, 1) || unique {
 			t.Errorf("%q: unexpected path:\ngot: path=%v weight=%f unique=%t\nwant:path=<nil> weight=+Inf unique=false",
 				test.Name, np, weight, unique)
 		}
 
-		paths, weight := pt.AllBetween(test.Query.From(), test.Query.To())
+		paths, weight := pt.AllBetween(test.Query.From().ID(), test.Query.To().ID())
 		if weight != test.Weight {
 			t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
 				test.Name, weight, test.Weight)
@@ -169,7 +169,7 @@ func TestDijkstraAllPaths(t *testing.T) {
 				test.Name, got, test.WantPaths)
 		}
 
-		nps, weight := pt.AllBetween(test.NoPathFor.From(), test.NoPathFor.To())
+		nps, weight := pt.AllBetween(test.NoPathFor.From().ID(), test.NoPathFor.To().ID())
 		if nps != nil || !math.IsInf(weight, 1) {
 			t.Errorf("%q: unexpected path:\ngot: paths=%v weight=%f\nwant:path=<nil> weight=+Inf",
 				test.Name, nps, weight)
diff --git a/graph/path/dynamic/dstarlite.go b/graph/path/dynamic/dstarlite.go
index 5e0a82dd..70b23dfc 100644
--- a/graph/path/dynamic/dstarlite.go
+++ b/graph/path/dynamic/dstarlite.go
@@ -99,12 +99,14 @@ func NewDStarLite(s, t graph.Node, g graph.Graph, h path.Heuristic, m WorldModel
 		}
 	}
 	for _, u := range d.model.Nodes() {
-		for _, v := range g.From(u) {
-			w := edgeWeight(d.weight, u, v)
+		uid := u.ID()
+		for _, v := range g.From(uid) {
+			vid := v.ID()
+			w := edgeWeight(d.weight, uid, vid)
 			if w < 0 {
 				panic("D* Lite: negative edge weight")
 			}
-			d.model.SetWeightedEdge(simple.WeightedEdge{F: u, T: d.model.Node(v.ID()), W: w})
+			d.model.SetWeightedEdge(simple.WeightedEdge{F: u, T: d.model.Node(vid), W: w})
 		}
 	}
 
@@ -120,8 +122,8 @@ func NewDStarLite(s, t graph.Node, g graph.Graph, h path.Heuristic, m WorldModel
 // edgeWeight is a helper function that returns the weight of the edge between
 // two connected nodes, u and v, using the provided weight function. It panics
 // if there is no edge between u and v.
-func edgeWeight(weight path.Weighting, u, v graph.Node) float64 {
-	w, ok := weight(u, v)
+func edgeWeight(weight path.Weighting, uid, vid int64) float64 {
+	w, ok := weight(uid, vid)
 	if !ok {
 		panic("D* Lite: unexpected invalid weight")
 	}
@@ -187,29 +189,33 @@ func (d *DStarLite) findShortestPath() {
 		if !u.key.less(d.keyFor(d.s)) && d.s.rhs <= d.s.g {
 			break
 		}
+		uid := u.ID()
 		switch kNew := d.keyFor(u); {
 		case u.key.less(kNew):
 			d.queue.update(u, kNew)
 		case u.g > u.rhs:
 			u.g = u.rhs
 			d.queue.remove(u)
-			for _, _s := range d.model.To(u) {
+			for _, _s := range d.model.To(uid) {
 				s := _s.(*dStarLiteNode)
-				if s.ID() != d.t.ID() {
-					s.rhs = math.Min(s.rhs, edgeWeight(d.model.Weight, s, u)+u.g)
+				sid := s.ID()
+				if sid != d.t.ID() {
+					s.rhs = math.Min(s.rhs, edgeWeight(d.model.Weight, sid, uid)+u.g)
 				}
 				d.update(s)
 			}
 		default:
 			gOld := u.g
 			u.g = math.Inf(1)
-			for _, _s := range append(d.model.To(u), u) {
+			for _, _s := range append(d.model.To(uid), u) {
 				s := _s.(*dStarLiteNode)
-				if s.rhs == edgeWeight(d.model.Weight, s, u)+gOld {
+				sid := s.ID()
+				if s.rhs == edgeWeight(d.model.Weight, sid, uid)+gOld {
 					if s.ID() != d.t.ID() {
 						s.rhs = math.Inf(1)
-						for _, t := range d.model.From(s) {
-							s.rhs = math.Min(s.rhs, edgeWeight(d.model.Weight, s, t)+t.(*dStarLiteNode).g)
+						for _, t := range d.model.From(sid) {
+							tid := t.ID()
+							s.rhs = math.Min(s.rhs, edgeWeight(d.model.Weight, sid, tid)+t.(*dStarLiteNode).g)
 						}
 					}
 				}
@@ -243,9 +249,10 @@ func (d *DStarLite) Step() bool {
 	min := math.Inf(1)
 
 	var next *dStarLiteNode
-	for _, _s := range d.model.From(d.s) {
+	dsid := d.s.ID()
+	for _, _s := range d.model.From(dsid) {
 		s := _s.(*dStarLiteNode)
-		w := edgeWeight(d.model.Weight, d.s, s) + s.g
+		w := edgeWeight(d.model.Weight, dsid, s.ID()) + s.g
 		if w < min || (w == min && s.rhs < rhs) {
 			next = s
 			min = w
@@ -294,24 +301,27 @@ func (d *DStarLite) UpdateWorld(changes []graph.Edge) {
 	d.last = d.s
 	for _, e := range changes {
 		from := e.From()
+		fid := from.ID()
 		to := e.To()
-		c, _ := d.weight(from, to)
+		tid := to.ID()
+		c, _ := d.weight(fid, tid)
 		if c < 0 {
 			panic("D* Lite: negative edge weight")
 		}
-		cOld, _ := d.model.Weight(from, to)
+		cOld, _ := d.model.Weight(fid, tid)
 		u := d.worldNodeFor(from)
 		v := d.worldNodeFor(to)
 		d.model.SetWeightedEdge(simple.WeightedEdge{F: u, T: v, W: c})
+		uid := u.ID()
 		if cOld > c {
-			if u.ID() != d.t.ID() {
+			if uid != d.t.ID() {
 				u.rhs = math.Min(u.rhs, c+v.g)
 			}
 		} else if u.rhs == cOld+v.g {
-			if u.ID() != d.t.ID() {
+			if uid != d.t.ID() {
 				u.rhs = math.Inf(1)
-				for _, t := range d.model.From(u) {
-					u.rhs = math.Min(u.rhs, edgeWeight(d.model.Weight, u, t)+t.(*dStarLiteNode).g)
+				for _, t := range d.model.From(uid) {
+					u.rhs = math.Min(u.rhs, edgeWeight(d.model.Weight, uid, t.ID())+t.(*dStarLiteNode).g)
 				}
 			}
 		}
@@ -354,9 +364,11 @@ func (d *DStarLite) Path() (p []graph.Node, weight float64) {
 			next *dStarLiteNode
 			cost float64
 		)
-		for _, _v := range d.model.From(u) {
+		uid := u.ID()
+		for _, _v := range d.model.From(uid) {
 			v := _v.(*dStarLiteNode)
-			w := edgeWeight(d.model.Weight, u, v)
+			vid := v.ID()
+			w := edgeWeight(d.model.Weight, uid, vid)
 			if rhs := w + v.g; rhs < min || (rhs == min && v.rhs < rhsMin) {
 				next = v
 				min = rhs
diff --git a/graph/path/dynamic/dstarlite_test.go b/graph/path/dynamic/dstarlite_test.go
index 495b31fc..90442d7b 100644
--- a/graph/path/dynamic/dstarlite_test.go
+++ b/graph/path/dynamic/dstarlite_test.go
@@ -389,7 +389,8 @@ var dynamicDStarLiteTests = []struct {
 			all := l.Grid.AllVisible
 			l.Grid.AllVisible = false
 			for _, n := range l.Nodes() {
-				l.Known[n.ID()] = !l.Grid.Has(n)
+				id := n.ID()
+				l.Known[id] = !l.Grid.Has(id)
 			}
 			l.Grid.AllVisible = all
 
@@ -401,19 +402,21 @@ var dynamicDStarLiteTests = []struct {
 
 			// Check we have a correctly modified representation.
 			for _, u := range l.Nodes() {
+				uid := u.ID()
 				for _, v := range l.Nodes() {
-					if l.HasEdgeBetween(u, v) != l.Grid.HasEdgeBetween(u, v) {
-						ur, uc := l.RowCol(u.ID())
-						vr, vc := l.RowCol(v.ID())
+					vid := v.ID()
+					if l.HasEdgeBetween(uid, vid) != l.Grid.HasEdgeBetween(uid, vid) {
+						ur, uc := l.RowCol(uid)
+						vr, vc := l.RowCol(vid)
 						if (ur == wallRow && uc == wallCol) || (vr == wallRow && vc == wallCol) {
-							if !l.HasEdgeBetween(u, v) {
+							if !l.HasEdgeBetween(uid, vid) {
 								panic(fmt.Sprintf("expected to believe edge between %v (%d,%d) and %v (%d,%d) is passable",
 									u, v, ur, uc, vr, vc))
 							}
 							continue
 						}
 						panic(fmt.Sprintf("disagreement about edge between %v (%d,%d) and %v (%d,%d): got:%t want:%t",
-							u, v, ur, uc, vr, vc, l.HasEdgeBetween(u, v), l.Grid.HasEdgeBetween(u, v)))
+							u, v, ur, uc, vr, vc, l.HasEdgeBetween(uid, vid), l.Grid.HasEdgeBetween(uid, vid)))
 					}
 				}
 			}
@@ -574,8 +577,8 @@ func TestDStarLiteDynamic(t *testing.T) {
 			l.MoveTo(test.s)
 
 			heuristic := func(a, b graph.Node) float64 {
-				ax, ay := l.XY(a)
-				bx, by := l.XY(b)
+				ax, ay := l.XY(a.ID())
+				bx, by := l.XY(b.ID())
 				return test.heuristic(ax-bx, ay-by)
 			}
 
@@ -657,7 +660,7 @@ func weightOf(path []graph.Node, g graph.Weighted) float64 {
 	var w float64
 	if len(path) > 1 {
 		for p, n := range path[1:] {
-			ew, ok := g.Weight(path[p], n)
+			ew, ok := g.Weight(path[p].ID(), n.ID())
 			if !ok {
 				return math.Inf(1)
 			}
@@ -673,7 +676,7 @@ func simpleWeightedEdgesOf(g graph.Weighted, edges []graph.Edge) []simple.Weight
 	for i, e := range edges {
 		w[i].F = e.From()
 		w[i].T = e.To()
-		ew, _ := g.Weight(e.From(), e.To())
+		ew, _ := g.Weight(e.From().ID(), e.To().ID())
 		w[i].W = ew
 	}
 	return w
diff --git a/graph/path/dynamic/dumper_test.go b/graph/path/dynamic/dumper_test.go
index 950d613e..b7fa9392 100644
--- a/graph/path/dynamic/dumper_test.go
+++ b/graph/path/dynamic/dumper_test.go
@@ -61,7 +61,7 @@ func (d *dumper) dump(withpath bool) {
 				switch ln {
 				case 0:
 					if n.ID() == d.grid.Location.ID() {
-						if d.grid.Grid.HasOpen(n) {
+						if d.grid.Grid.HasOpen(n.ID()) {
 							fmt.Fprintf(w, "id:%2d  >@<", n.ID())
 						} else {
 							// Mark location as illegal.
@@ -70,19 +70,19 @@ func (d *dumper) dump(withpath bool) {
 					} else if n.ID() == d.dStarLite.t.ID() {
 						fmt.Fprintf(w, "id:%2d   G", n.ID())
 						// Mark goal cell as illegal.
-						if !d.grid.Grid.HasOpen(n) {
+						if !d.grid.Grid.HasOpen(n.ID()) {
 							fmt.Fprint(w, "!")
 						}
 					} else if pathStep[n.ID()] > 0 {
 						fmt.Fprintf(w, "id:%2d  %2d", n.ID(), pathStep[n.ID()])
 						// Mark path cells with an obstruction.
-						if !d.grid.Grid.HasOpen(n) {
+						if !d.grid.Grid.HasOpen(n.ID()) {
 							fmt.Fprint(w, "!")
 						}
 					} else {
 						fmt.Fprintf(w, "id:%2d", n.ID())
 						// Mark cells with an obstruction.
-						if !d.grid.Grid.HasOpen(n) {
+						if !d.grid.Grid.HasOpen(n.ID()) {
 							fmt.Fprint(w, "   *")
 						}
 					}
diff --git a/graph/path/floydwarshall.go b/graph/path/floydwarshall.go
index 1ffe25bd..db9d9148 100644
--- a/graph/path/floydwarshall.go
+++ b/graph/path/floydwarshall.go
@@ -23,9 +23,11 @@ func FloydWarshall(g graph.Graph) (paths AllShortest, ok bool) {
 	paths = newAllShortest(nodes, true)
 	for i, u := range nodes {
 		paths.dist.Set(i, i, 0)
-		for _, v := range g.From(u) {
-			j := paths.indexOf[v.ID()]
-			w, ok := weight(u, v)
+		uid := u.ID()
+		for _, v := range g.From(uid) {
+			vid := v.ID()
+			j := paths.indexOf[vid]
+			w, ok := weight(uid, vid)
 			if !ok {
 				panic("floyd-warshall: unexpected invalid weight")
 			}
diff --git a/graph/path/floydwarshall_test.go b/graph/path/floydwarshall_test.go
index 3947ad2e..45dc1b2e 100644
--- a/graph/path/floydwarshall_test.go
+++ b/graph/path/floydwarshall_test.go
@@ -35,12 +35,12 @@ func TestFloydWarshall(t *testing.T) {
 
 		// Check all random paths returned are OK.
 		for i := 0; i < 10; i++ {
-			p, weight, unique := pt.Between(test.Query.From(), test.Query.To())
+			p, weight, unique := pt.Between(test.Query.From().ID(), test.Query.To().ID())
 			if weight != test.Weight {
 				t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
 					test.Name, weight, test.Weight)
 			}
-			if weight := pt.Weight(test.Query.From(), test.Query.To()); weight != test.Weight {
+			if weight := pt.Weight(test.Query.From().ID(), test.Query.To().ID()); weight != test.Weight {
 				t.Errorf("%q: unexpected weight from Weight: got:%f want:%f",
 					test.Name, weight, test.Weight)
 			}
@@ -66,13 +66,13 @@ func TestFloydWarshall(t *testing.T) {
 			}
 		}
 
-		np, weight, unique := pt.Between(test.NoPathFor.From(), test.NoPathFor.To())
+		np, weight, unique := pt.Between(test.NoPathFor.From().ID(), test.NoPathFor.To().ID())
 		if np != nil || !math.IsInf(weight, 1) || unique {
 			t.Errorf("%q: unexpected path:\ngot: path=%v weight=%f unique=%t\nwant:path=<nil> weight=+Inf unique=false",
 				test.Name, np, weight, unique)
 		}
 
-		paths, weight := pt.AllBetween(test.Query.From(), test.Query.To())
+		paths, weight := pt.AllBetween(test.Query.From().ID(), test.Query.To().ID())
 		if weight != test.Weight {
 			t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
 				test.Name, weight, test.Weight)
@@ -93,7 +93,7 @@ func TestFloydWarshall(t *testing.T) {
 				test.Name, got, test.WantPaths)
 		}
 
-		nps, weight := pt.AllBetween(test.NoPathFor.From(), test.NoPathFor.To())
+		nps, weight := pt.AllBetween(test.NoPathFor.From().ID(), test.NoPathFor.To().ID())
 		if nps != nil || !math.IsInf(weight, 1) {
 			t.Errorf("%q: unexpected path:\ngot: paths=%v weight=%f\nwant:path=<nil> weight=+Inf",
 				test.Name, nps, weight)
diff --git a/graph/path/internal/grid.go b/graph/path/internal/grid.go
index cc7e1366..f062c049 100644
--- a/graph/path/internal/grid.go
+++ b/graph/path/internal/grid.go
@@ -104,17 +104,12 @@ func (g *Grid) Nodes() []graph.Node {
 // Has returns whether n is a node in the grid. The state of
 // the AllVisible field determines whether a non-open node is
 // present.
-func (g *Grid) Has(n graph.Node) bool {
-	return g.has(n.ID())
-}
-
-func (g *Grid) has(id int64) bool {
+func (g *Grid) Has(id int64) bool {
 	return 0 <= id && id < int64(len(g.open)) && (g.AllVisible || g.open[id])
 }
 
 // HasOpen returns whether n is an open node in the grid.
-func (g *Grid) HasOpen(n graph.Node) bool {
-	id := n.ID()
+func (g *Grid) HasOpen(id int64) bool {
 	return 0 <= id && id < int64(len(g.open)) && g.open[id]
 }
 
@@ -145,11 +140,11 @@ func (g *Grid) RowCol(id int64) (r, c int) {
 
 // XY returns the cartesian coordinates of n. If n is not a node
 // in the grid, (NaN, NaN) is returned.
-func (g *Grid) XY(n graph.Node) (x, y float64) {
-	if !g.Has(n) {
+func (g *Grid) XY(id int64) (x, y float64) {
+	if !g.Has(id) {
 		return math.NaN(), math.NaN()
 	}
-	r, c := g.RowCol(n.ID())
+	r, c := g.RowCol(id)
 	return float64(c), float64(r)
 }
 
@@ -163,15 +158,15 @@ func (g *Grid) NodeAt(r, c int) graph.Node {
 
 // From returns all the nodes reachable from u. Reachabilty requires that both
 // ends of an edge must be open.
-func (g *Grid) From(u graph.Node) []graph.Node {
-	if !g.HasOpen(u) {
+func (g *Grid) From(uid int64) []graph.Node {
+	if !g.HasOpen(uid) {
 		return nil
 	}
-	nr, nc := g.RowCol(u.ID())
+	nr, nc := g.RowCol(uid)
 	var to []graph.Node
 	for r := nr - 1; r <= nr+1; r++ {
 		for c := nc - 1; c <= nc+1; c++ {
-			if v := g.NodeAt(r, c); v != nil && g.HasEdgeBetween(u, v) {
+			if v := g.NodeAt(r, c); v != nil && g.HasEdgeBetween(uid, v.ID()) {
 				to = append(to, v)
 			}
 		}
@@ -180,12 +175,12 @@ func (g *Grid) From(u graph.Node) []graph.Node {
 }
 
 // HasEdgeBetween returns whether there is an edge between u and v.
-func (g *Grid) HasEdgeBetween(u, v graph.Node) bool {
-	if !g.HasOpen(u) || !g.HasOpen(v) || u.ID() == v.ID() {
+func (g *Grid) HasEdgeBetween(uid, vid int64) bool {
+	if !g.HasOpen(uid) || !g.HasOpen(vid) || uid == vid {
 		return false
 	}
-	ur, uc := g.RowCol(u.ID())
-	vr, vc := g.RowCol(v.ID())
+	ur, uc := g.RowCol(uid)
+	vr, vc := g.RowCol(vid)
 	if abs(ur-vr) > 1 || abs(uc-vc) > 1 {
 		return false
 	}
@@ -200,47 +195,47 @@ func abs(i int) int {
 }
 
 // Edge returns the edge between u and v.
-func (g *Grid) Edge(u, v graph.Node) graph.Edge {
-	return g.WeightedEdgeBetween(u, v)
+func (g *Grid) Edge(uid, vid int64) graph.Edge {
+	return g.WeightedEdgeBetween(uid, vid)
 }
 
 // WeightedEdge returns the weighted edge between u and v.
-func (g *Grid) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
-	return g.WeightedEdgeBetween(u, v)
+func (g *Grid) WeightedEdge(uid, vid int64) graph.WeightedEdge {
+	return g.WeightedEdgeBetween(uid, vid)
 }
 
 // EdgeBetween returns the edge between u and v.
-func (g *Grid) EdgeBetween(u, v graph.Node) graph.Edge {
-	return g.WeightedEdgeBetween(u, v)
+func (g *Grid) EdgeBetween(uid, vid int64) graph.Edge {
+	return g.WeightedEdgeBetween(uid, vid)
 }
 
 // WeightedEdgeBetween returns the weighted edge between u and v.
-func (g *Grid) WeightedEdgeBetween(u, v graph.Node) graph.WeightedEdge {
-	if g.HasEdgeBetween(u, v) {
+func (g *Grid) WeightedEdgeBetween(uid, vid int64) graph.WeightedEdge {
+	if g.HasEdgeBetween(uid, vid) {
 		if !g.AllowDiagonal || g.UnitEdgeWeight {
-			return simple.WeightedEdge{F: u, T: v, W: 1}
+			return simple.WeightedEdge{F: simple.Node(uid), T: simple.Node(vid), W: 1}
 		}
-		ux, uy := g.XY(u)
-		vx, vy := g.XY(v)
-		return simple.WeightedEdge{F: u, T: v, W: math.Hypot(ux-vx, uy-vy)}
+		ux, uy := g.XY(uid)
+		vx, vy := g.XY(vid)
+		return simple.WeightedEdge{F: simple.Node(uid), T: simple.Node(vid), W: math.Hypot(ux-vx, uy-vy)}
 	}
 	return nil
 }
 
 // Weight returns the weight of the given edge.
-func (g *Grid) Weight(x, y graph.Node) (w float64, ok bool) {
-	if x.ID() == y.ID() {
+func (g *Grid) Weight(xid, yid int64) (w float64, ok bool) {
+	if xid == yid {
 		return 0, true
 	}
-	if !g.HasEdgeBetween(x, y) {
+	if !g.HasEdgeBetween(xid, yid) {
 		return math.Inf(1), false
 	}
-	if e := g.EdgeBetween(x, y); e != nil {
+	if e := g.EdgeBetween(xid, yid); e != nil {
 		if !g.AllowDiagonal || g.UnitEdgeWeight {
 			return 1, true
 		}
-		ux, uy := g.XY(e.From())
-		vx, vy := g.XY(e.To())
+		ux, uy := g.XY(e.From().ID())
+		vx, vy := g.XY(e.To().ID())
 		return math.Hypot(ux-vx, uy-vy), true
 	}
 	return math.Inf(1), true
@@ -274,15 +269,15 @@ func (g *Grid) Render(path []graph.Node) ([]byte, error) {
 	// We don't use topo.IsPathIn at the outset because we
 	// want to draw as much as possible before failing.
 	for i, n := range path {
-		if !g.Has(n) || (i != 0 && !g.HasEdgeBetween(path[i-1], n)) {
-			id := n.ID()
+		id := n.ID()
+		if !g.Has(id) || (i != 0 && !g.HasEdgeBetween(path[i-1].ID(), id)) {
 			if 0 <= id && id < int64(len(g.open)) {
-				r, c := g.RowCol(n.ID())
+				r, c := g.RowCol(id)
 				b[r*(g.c+1)+c] = '!'
 			}
 			return b, errors.New("grid: not a path in graph")
 		}
-		r, c := g.RowCol(n.ID())
+		r, c := g.RowCol(id)
 		switch i {
 		case len(path) - 1:
 			b[r*(g.c+1)+c] = 'G'
diff --git a/graph/path/internal/grid_test.go b/graph/path/internal/grid_test.go
index 3034bba3..7132ffed 100644
--- a/graph/path/internal/grid_test.go
+++ b/graph/path/internal/grid_test.go
@@ -249,7 +249,7 @@ func TestGrid(t *testing.T) {
 	}
 	for _, test := range reach {
 		g.AllowDiagonal = test.diagonal
-		got := g.From(test.from)
+		got := g.From(test.from.ID())
 		if !reflect.DeepEqual(got, test.to) {
 			t.Fatalf("unexpected nodes from %d with allow diagonal=%t:\ngot: %v\nwant:%v",
 				test.from, test.diagonal, got, test.to)
diff --git a/graph/path/internal/limited.go b/graph/path/internal/limited.go
index 8f86a473..6e2cfcdb 100644
--- a/graph/path/internal/limited.go
+++ b/graph/path/internal/limited.go
@@ -47,23 +47,25 @@ func (l *LimitedVisionGrid) MoveTo(n graph.Node) (new, old []graph.Edge) {
 			if u == nil {
 				continue
 			}
-			ux, uy := l.XY(u)
+			uid := u.ID()
+			ux, uy := l.XY(uid)
 			if math.Hypot(x-ux, y-uy) > l.VisionRadius {
 				continue
 			}
-			for _, v := range l.allPossibleFrom(u) {
-				if seen[[2]int64{u.ID(), v.ID()}] {
+			for _, v := range l.allPossibleFrom(uid) {
+				vid := v.ID()
+				if seen[[2]int64{uid, vid}] {
 					continue
 				}
-				seen[[2]int64{u.ID(), v.ID()}] = true
+				seen[[2]int64{uid, vid}] = true
 
-				vx, vy := l.XY(v)
-				if !l.Known[v.ID()] && math.Hypot(x-vx, y-vy) > l.VisionRadius {
+				vx, vy := l.XY(vid)
+				if !l.Known[vid] && math.Hypot(x-vx, y-vy) > l.VisionRadius {
 					continue
 				}
 
 				e := simple.Edge{F: u, T: v}
-				if !l.Known[u.ID()] || !l.Known[v.ID()] {
+				if !l.Known[uid] || !l.Known[vid] {
 					new = append(new, e)
 				} else {
 					old = append(old, e)
@@ -79,18 +81,20 @@ func (l *LimitedVisionGrid) MoveTo(n graph.Node) (new, old []graph.Edge) {
 				if u == nil {
 					continue
 				}
-				ux, uy := l.XY(u)
+				uid := u.ID()
+				ux, uy := l.XY(uid)
 				if math.Hypot(x-ux, y-uy) > l.VisionRadius {
 					continue
 				}
-				for _, v := range l.allPossibleFrom(u) {
-					vx, vy := l.XY(v)
+				for _, v := range l.allPossibleFrom(uid) {
+					vid := v.ID()
+					vx, vy := l.XY(vid)
 					if math.Hypot(x-vx, y-vy) > l.VisionRadius {
 						continue
 					}
-					l.Known[v.ID()] = true
+					l.Known[vid] = true
 				}
-				l.Known[u.ID()] = true
+				l.Known[uid] = true
 			}
 		}
 
@@ -100,19 +104,19 @@ func (l *LimitedVisionGrid) MoveTo(n graph.Node) (new, old []graph.Edge) {
 }
 
 // allPossibleFrom returns all the nodes possibly reachable from u.
-func (l *LimitedVisionGrid) allPossibleFrom(u graph.Node) []graph.Node {
-	if !l.Has(u) {
+func (l *LimitedVisionGrid) allPossibleFrom(uid int64) []graph.Node {
+	if !l.Has(uid) {
 		return nil
 	}
-	nr, nc := l.RowCol(u.ID())
+	nr, nc := l.RowCol(uid)
 	var to []graph.Node
 	for r := nr - 1; r <= nr+1; r++ {
 		for c := nc - 1; c <= nc+1; c++ {
 			v := l.NodeAt(r, c)
-			if v == nil || u.ID() == v.ID() {
+			if v == nil || uid == v.ID() {
 				continue
 			}
-			ur, uc := l.RowCol(u.ID())
+			ur, uc := l.RowCol(uid)
 			vr, vc := l.RowCol(v.ID())
 			if abs(ur-vr) > 1 || abs(uc-vc) > 1 {
 				continue
@@ -134,11 +138,11 @@ func (l *LimitedVisionGrid) RowCol(id int64) (r, c int) {
 
 // XY returns the cartesian coordinates of n. If n is not a node
 // in the grid, (NaN, NaN) is returned.
-func (l *LimitedVisionGrid) XY(n graph.Node) (x, y float64) {
-	if !l.Has(n) {
+func (l *LimitedVisionGrid) XY(id int64) (x, y float64) {
+	if !l.Has(id) {
 		return math.NaN(), math.NaN()
 	}
-	r, c := l.RowCol(n.ID())
+	r, c := l.RowCol(id)
 	return float64(c), float64(r)
 }
 
@@ -157,25 +161,21 @@ func (l *LimitedVisionGrid) NodeAt(r, c int) graph.Node {
 }
 
 // Has returns whether n is a node in the grid.
-func (l *LimitedVisionGrid) Has(n graph.Node) bool {
-	return l.has(n.ID())
-}
-
-func (l *LimitedVisionGrid) has(id int64) bool {
+func (l *LimitedVisionGrid) Has(id int64) bool {
 	return 0 <= id && id < int64(len(l.Grid.open))
 }
 
 // From returns nodes that are optimistically reachable from u.
-func (l *LimitedVisionGrid) From(u graph.Node) []graph.Node {
-	if !l.Has(u) {
+func (l *LimitedVisionGrid) From(uid int64) []graph.Node {
+	if !l.Has(uid) {
 		return nil
 	}
 
-	nr, nc := l.RowCol(u.ID())
+	nr, nc := l.RowCol(uid)
 	var to []graph.Node
 	for r := nr - 1; r <= nr+1; r++ {
 		for c := nc - 1; c <= nc+1; c++ {
-			if v := l.NodeAt(r, c); v != nil && l.HasEdgeBetween(u, v) {
+			if v := l.NodeAt(r, c); v != nil && l.HasEdgeBetween(uid, v.ID()) {
 				to = append(to, v)
 			}
 		}
@@ -184,12 +184,12 @@ func (l *LimitedVisionGrid) From(u graph.Node) []graph.Node {
 }
 
 // HasEdgeBetween optimistically returns whether an edge is exists between u and v.
-func (l *LimitedVisionGrid) HasEdgeBetween(u, v graph.Node) bool {
-	if u.ID() == v.ID() {
+func (l *LimitedVisionGrid) HasEdgeBetween(uid, vid int64) bool {
+	if uid == vid {
 		return false
 	}
-	ur, uc := l.RowCol(u.ID())
-	vr, vc := l.RowCol(v.ID())
+	ur, uc := l.RowCol(uid)
+	vr, vc := l.RowCol(vid)
 	if abs(ur-vr) > 1 || abs(uc-vc) > 1 {
 		return false
 	}
@@ -197,66 +197,66 @@ func (l *LimitedVisionGrid) HasEdgeBetween(u, v graph.Node) bool {
 		return false
 	}
 
-	x, y := l.XY(l.Location)
-	ux, uy := l.XY(u)
-	vx, vy := l.XY(v)
-	uKnown := l.Known[u.ID()] || math.Hypot(x-ux, y-uy) <= l.VisionRadius
-	vKnown := l.Known[v.ID()] || math.Hypot(x-vx, y-vy) <= l.VisionRadius
+	x, y := l.XY(l.Location.ID())
+	ux, uy := l.XY(uid)
+	vx, vy := l.XY(vid)
+	uKnown := l.Known[uid] || math.Hypot(x-ux, y-uy) <= l.VisionRadius
+	vKnown := l.Known[vid] || math.Hypot(x-vx, y-vy) <= l.VisionRadius
 
 	switch {
 	case uKnown && vKnown:
-		return l.Grid.HasEdgeBetween(u, v)
+		return l.Grid.HasEdgeBetween(uid, vid)
 	case uKnown:
-		return l.Grid.HasOpen(u)
+		return l.Grid.HasOpen(uid)
 	case vKnown:
-		return l.Grid.HasOpen(v)
+		return l.Grid.HasOpen(vid)
 	default:
 		return true
 	}
 }
 
 // Edge optimistically returns the edge from u to v.
-func (l *LimitedVisionGrid) Edge(u, v graph.Node) graph.Edge {
-	return l.WeightedEdgeBetween(u, v)
+func (l *LimitedVisionGrid) Edge(uid, vid int64) graph.Edge {
+	return l.WeightedEdgeBetween(uid, vid)
 }
 
 // Edge optimistically returns the weighted edge from u to v.
-func (l *LimitedVisionGrid) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
-	return l.WeightedEdgeBetween(u, v)
+func (l *LimitedVisionGrid) WeightedEdge(uid, vid int64) graph.WeightedEdge {
+	return l.WeightedEdgeBetween(uid, vid)
 }
 
 // WeightedEdgeBetween optimistically returns the edge between u and v.
-func (l *LimitedVisionGrid) EdgeBetween(u, v graph.Node) graph.Edge {
-	return l.WeightedEdgeBetween(u, v)
+func (l *LimitedVisionGrid) EdgeBetween(uid, vid int64) graph.Edge {
+	return l.WeightedEdgeBetween(uid, vid)
 }
 
 // WeightedEdgeBetween optimistically returns the weighted edge between u and v.
-func (l *LimitedVisionGrid) WeightedEdgeBetween(u, v graph.Node) graph.WeightedEdge {
-	if l.HasEdgeBetween(u, v) {
+func (l *LimitedVisionGrid) WeightedEdgeBetween(uid, vid int64) graph.WeightedEdge {
+	if l.HasEdgeBetween(uid, vid) {
 		if !l.Grid.AllowDiagonal || l.Grid.UnitEdgeWeight {
-			return simple.WeightedEdge{F: u, T: v, W: 1}
+			return simple.WeightedEdge{F: simple.Node(uid), T: simple.Node(vid), W: 1}
 		}
-		ux, uy := l.XY(u)
-		vx, vy := l.XY(v)
-		return simple.WeightedEdge{F: u, T: v, W: math.Hypot(ux-vx, uy-vy)}
+		ux, uy := l.XY(uid)
+		vx, vy := l.XY(vid)
+		return simple.WeightedEdge{F: simple.Node(uid), T: simple.Node(vid), W: math.Hypot(ux-vx, uy-vy)}
 	}
 	return nil
 }
 
 // Weight returns the weight of the given edge.
-func (l *LimitedVisionGrid) Weight(x, y graph.Node) (w float64, ok bool) {
-	if x.ID() == y.ID() {
+func (l *LimitedVisionGrid) Weight(xid, yid int64) (w float64, ok bool) {
+	if xid == yid {
 		return 0, true
 	}
-	if !l.HasEdgeBetween(x, y) {
+	if !l.HasEdgeBetween(xid, yid) {
 		return math.Inf(1), false
 	}
-	if e := l.EdgeBetween(x, y); e != nil {
+	if e := l.EdgeBetween(xid, yid); e != nil {
 		if !l.Grid.AllowDiagonal || l.Grid.UnitEdgeWeight {
 			return 1, true
 		}
-		ux, uy := l.XY(e.From())
-		vx, vy := l.XY(e.To())
+		ux, uy := l.XY(e.From().ID())
+		vx, vy := l.XY(e.To().ID())
 		return math.Hypot(ux-vx, uy-vy), true
 
 	}
@@ -294,15 +294,15 @@ func (l *LimitedVisionGrid) Render(path []graph.Node) ([]byte, error) {
 	// We don't use topo.IsPathIn at the outset because we
 	// want to draw as much as possible before failing.
 	for i, n := range path {
-		if !l.Has(n) || (i != 0 && !l.HasEdgeBetween(path[i-1], n)) {
-			id := n.ID()
+		id := n.ID()
+		if !l.Has(id) || (i != 0 && !l.HasEdgeBetween(path[i-1].ID(), id)) {
 			if 0 <= id && id < int64(len(l.Grid.open)) {
-				r, c := l.RowCol(n.ID())
+				r, c := l.RowCol(id)
 				b[r*(cols+1)+c] = '!'
 			}
 			return b, errors.New("grid: not a path in graph")
 		}
-		r, c := l.RowCol(n.ID())
+		r, c := l.RowCol(id)
 		switch i {
 		case len(path) - 1:
 			b[r*(cols+1)+c] = 'G'
diff --git a/graph/path/internal/limited_test.go b/graph/path/internal/limited_test.go
index 8fa3efde..6372471d 100644
--- a/graph/path/internal/limited_test.go
+++ b/graph/path/internal/limited_test.go
@@ -1165,23 +1165,25 @@ func TestLimitedVisionGrid(t *testing.T) {
 		}
 		l.Grid.AllowDiagonal = test.diag
 
-		x, y := l.XY(test.path[0])
+		x, y := l.XY(test.path[0].ID())
 		for _, u := range l.Nodes() {
-			ux, uy := l.XY(u)
+			uid := u.ID()
+			ux, uy := l.XY(uid)
 			uNear := math.Hypot(x-ux, y-uy) <= test.radius
 			for _, v := range l.Nodes() {
-				vx, vy := l.XY(v)
+				vid := v.ID()
+				vx, vy := l.XY(vid)
 				vNear := math.Hypot(x-vx, y-vy) <= test.radius
-				if u.ID() == v.ID() && l.HasEdgeBetween(u, v) {
+				if u.ID() == v.ID() && l.HasEdgeBetween(uid, vid) {
 					t.Errorf("unexpected self edge: %v -- %v", u, v)
 				}
-				if !uNear && !vNear && !l.HasEdgeBetween(u, v) && couldConnectIn(l, u, v) {
+				if !uNear && !vNear && !l.HasEdgeBetween(uid, vid) && couldConnectIn(l, uid, vid) {
 					t.Errorf("unexpected pessimism: no hope in distant edge between %v and %v for test %d",
 						u, v, i)
 				}
-				if (uNear && vNear) && l.HasEdgeBetween(u, v) != l.Grid.HasEdgeBetween(u, v) {
+				if (uNear && vNear) && l.HasEdgeBetween(uid, vid) != l.Grid.HasEdgeBetween(uid, vid) {
 					t.Errorf("unrealistic optimism: disagreement about edge between %v and %v for test %d: got:%t want:%t",
-						u, v, i, l.HasEdgeBetween(u, v), l.Grid.HasEdgeBetween(u, v))
+						u, v, i, l.HasEdgeBetween(uid, vid), l.Grid.HasEdgeBetween(uid, vid))
 				}
 			}
 		}
@@ -1205,7 +1207,7 @@ func asConcreteEdges(changes []graph.Edge, in graph.Weighted) []simple.WeightedE
 	for i, e := range changes {
 		we[i].F = e.From()
 		we[i].T = e.To()
-		w, ok := in.Weight(e.From(), e.To())
+		w, ok := in.Weight(e.From().ID(), e.To().ID())
 		if !ok && !math.IsInf(w, 1) {
 			panic("unexpected invalid finite weight")
 		}
@@ -1214,13 +1216,13 @@ func asConcreteEdges(changes []graph.Edge, in graph.Weighted) []simple.WeightedE
 	return we
 }
 
-func couldConnectIn(l *LimitedVisionGrid, u, v graph.Node) bool {
-	if u.ID() == v.ID() {
+func couldConnectIn(l *LimitedVisionGrid, uid, vid int64) bool {
+	if uid == vid {
 		return false
 	}
 
-	ur, uc := l.RowCol(u.ID())
-	vr, vc := l.RowCol(v.ID())
+	ur, uc := l.RowCol(uid)
+	vr, vc := l.RowCol(vid)
 	if abs(ur-vr) > 1 || abs(uc-vc) > 1 {
 		return false
 	}
@@ -1228,13 +1230,13 @@ func couldConnectIn(l *LimitedVisionGrid, u, v graph.Node) bool {
 		return false
 	}
 
-	if !l.Known[u.ID()] && !l.Known[v.ID()] {
+	if !l.Known[uid] && !l.Known[vid] {
 		return true
 	}
-	if l.Known[u.ID()] && !l.Grid.HasOpen(u) {
+	if l.Known[uid] && !l.Grid.HasOpen(uid) {
 		return false
 	}
-	if l.Known[v.ID()] && !l.Grid.HasOpen(v) {
+	if l.Known[vid] && !l.Grid.HasOpen(vid) {
 		return false
 	}
 
diff --git a/graph/path/johnson_apsp.go b/graph/path/johnson_apsp.go
index cf064696..4902d323 100644
--- a/graph/path/johnson_apsp.go
+++ b/graph/path/johnson_apsp.go
@@ -52,12 +52,12 @@ func JohnsonAllPaths(g graph.Graph) (paths AllShortest, ok bool) {
 	dijkstraAllPaths(jg, paths)
 
 	for i, u := range paths.nodes {
-		hu := jg.adjustBy.WeightTo(u)
+		hu := jg.adjustBy.WeightTo(u.ID())
 		for j, v := range paths.nodes {
 			if i == j {
 				continue
 			}
-			hv := jg.adjustBy.WeightTo(v)
+			hv := jg.adjustBy.WeightTo(v.ID())
 			paths.dist.Set(i, j, paths.dist.At(i, j)-hu+hv)
 		}
 	}
@@ -69,8 +69,8 @@ type johnsonWeightAdjuster struct {
 	q int64
 	g graph.Graph
 
-	from   func(graph.Node) []graph.Node
-	edgeTo func(graph.Node, graph.Node) graph.Edge
+	from   func(id int64) []graph.Node
+	edgeTo func(uid, vid int64) graph.Edge
 	weight Weighting
 
 	bellmanFord bool
@@ -86,11 +86,11 @@ var (
 	_ graph.Weighted = johnsonWeightAdjuster{}
 )
 
-func (g johnsonWeightAdjuster) Has(n graph.Node) bool {
-	if g.bellmanFord && n.ID() == g.q {
+func (g johnsonWeightAdjuster) Has(id int64) bool {
+	if g.bellmanFord && id == g.q {
 		return true
 	}
-	return g.g.Has(n)
+	return g.g.Has(id)
 
 }
 
@@ -101,40 +101,40 @@ func (g johnsonWeightAdjuster) Nodes() []graph.Node {
 	return g.g.Nodes()
 }
 
-func (g johnsonWeightAdjuster) From(n graph.Node) []graph.Node {
-	if g.bellmanFord && n.ID() == g.q {
+func (g johnsonWeightAdjuster) From(id int64) []graph.Node {
+	if g.bellmanFord && id == g.q {
 		return g.g.Nodes()
 	}
-	return g.from(n)
+	return g.from(id)
 }
 
-func (g johnsonWeightAdjuster) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
+func (g johnsonWeightAdjuster) WeightedEdge(_, _ int64) graph.WeightedEdge {
 	panic("path: unintended use of johnsonWeightAdjuster")
 }
 
-func (g johnsonWeightAdjuster) Edge(u, v graph.Node) graph.Edge {
-	if g.bellmanFord && u.ID() == g.q && g.g.Has(v) {
-		return simple.Edge{F: johnsonGraphNode(g.q), T: v}
+func (g johnsonWeightAdjuster) Edge(uid, vid int64) graph.Edge {
+	if g.bellmanFord && uid == g.q && g.g.Has(vid) {
+		return simple.Edge{F: johnsonGraphNode(g.q), T: simple.Node(vid)}
 	}
-	return g.edgeTo(u, v)
+	return g.edgeTo(uid, vid)
 }
 
-func (g johnsonWeightAdjuster) Weight(x, y graph.Node) (w float64, ok bool) {
+func (g johnsonWeightAdjuster) Weight(xid, yid int64) (w float64, ok bool) {
 	if g.bellmanFord {
 		switch g.q {
-		case x.ID():
+		case xid:
 			return 0, true
-		case y.ID():
+		case yid:
 			return math.Inf(1), false
 		default:
-			return g.weight(x, y)
+			return g.weight(xid, yid)
 		}
 	}
-	w, ok = g.weight(x, y)
-	return w + g.adjustBy.WeightTo(x) - g.adjustBy.WeightTo(y), ok
+	w, ok = g.weight(xid, yid)
+	return w + g.adjustBy.WeightTo(xid) - g.adjustBy.WeightTo(yid), ok
 }
 
-func (johnsonWeightAdjuster) HasEdgeBetween(_, _ graph.Node) bool {
+func (johnsonWeightAdjuster) HasEdgeBetween(_, _ int64) bool {
 	panic("path: unintended use of johnsonWeightAdjuster")
 }
 
diff --git a/graph/path/johnson_apsp_test.go b/graph/path/johnson_apsp_test.go
index fcf62046..ca764863 100644
--- a/graph/path/johnson_apsp_test.go
+++ b/graph/path/johnson_apsp_test.go
@@ -35,12 +35,12 @@ func TestJohnsonAllPaths(t *testing.T) {
 
 		// Check all random paths returned are OK.
 		for i := 0; i < 10; i++ {
-			p, weight, unique := pt.Between(test.Query.From(), test.Query.To())
+			p, weight, unique := pt.Between(test.Query.From().ID(), test.Query.To().ID())
 			if weight != test.Weight {
 				t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
 					test.Name, weight, test.Weight)
 			}
-			if weight := pt.Weight(test.Query.From(), test.Query.To()); weight != test.Weight {
+			if weight := pt.Weight(test.Query.From().ID(), test.Query.To().ID()); weight != test.Weight {
 				t.Errorf("%q: unexpected weight from Weight: got:%f want:%f",
 					test.Name, weight, test.Weight)
 			}
@@ -66,13 +66,13 @@ func TestJohnsonAllPaths(t *testing.T) {
 			}
 		}
 
-		np, weight, unique := pt.Between(test.NoPathFor.From(), test.NoPathFor.To())
+		np, weight, unique := pt.Between(test.NoPathFor.From().ID(), test.NoPathFor.To().ID())
 		if np != nil || !math.IsInf(weight, 1) || unique {
 			t.Errorf("%q: unexpected path:\ngot: path=%v weight=%f unique=%t\nwant:path=<nil> weight=+Inf unique=false",
 				test.Name, np, weight, unique)
 		}
 
-		paths, weight := pt.AllBetween(test.Query.From(), test.Query.To())
+		paths, weight := pt.AllBetween(test.Query.From().ID(), test.Query.To().ID())
 		if weight != test.Weight {
 			t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
 				test.Name, weight, test.Weight)
@@ -93,7 +93,7 @@ func TestJohnsonAllPaths(t *testing.T) {
 				test.Name, got, test.WantPaths)
 		}
 
-		nps, weight := pt.AllBetween(test.NoPathFor.From(), test.NoPathFor.To())
+		nps, weight := pt.AllBetween(test.NoPathFor.From().ID(), test.NoPathFor.To().ID())
 		if nps != nil || !math.IsInf(weight, 1) {
 			t.Errorf("%q: unexpected path:\ngot: paths=%v weight=%f\nwant:path=<nil> weight=+Inf",
 				test.Name, nps, weight)
diff --git a/graph/path/negative_cycles_example_test.go b/graph/path/negative_cycles_example_test.go
index 91273dc4..f70d3f43 100644
--- a/graph/path/negative_cycles_example_test.go
+++ b/graph/path/negative_cycles_example_test.go
@@ -47,7 +47,7 @@ func ExampleBellmanFordFrom_negativecycles() {
 		return
 	}
 	for _, n := range []simple.Node{'a', 'b', 'c', 'd', 'e', 'f'} {
-		p, w := pt.To(n)
+		p, w := pt.To(n.ID())
 		if math.IsNaN(w) {
 			fmt.Printf("negative cycle in path to %c path:%c\n", n, p)
 		}
diff --git a/graph/path/shortest.go b/graph/path/shortest.go
index 33876c6f..c2d120d4 100644
--- a/graph/path/shortest.go
+++ b/graph/path/shortest.go
@@ -93,8 +93,8 @@ func (p Shortest) From() graph.Node { return p.from }
 
 // WeightTo returns the weight of the minimum path to v. If the path to v includes
 // a negative cycle, the returned weight will not reflect the true path weight.
-func (p Shortest) WeightTo(v graph.Node) float64 {
-	to, toOK := p.indexOf[v.ID()]
+func (p Shortest) WeightTo(vid int64) float64 {
+	to, toOK := p.indexOf[vid]
 	if !toOK {
 		return math.Inf(1)
 	}
@@ -104,8 +104,8 @@ func (p Shortest) WeightTo(v graph.Node) float64 {
 // To returns a shortest path to v and the weight of the path. If the path
 // to v includes a negative cycle, one pass through the cycle will be included
 // in path and weight will be returned as NaN.
-func (p Shortest) To(v graph.Node) (path []graph.Node, weight float64) {
-	to, toOK := p.indexOf[v.ID()]
+func (p Shortest) To(vid int64) (path []graph.Node, weight float64) {
+	to, toOK := p.indexOf[vid]
 	if !toOK || math.IsInf(p.dist[to], 1) {
 		return nil, math.Inf(1)
 	}
@@ -136,7 +136,7 @@ func (p Shortest) To(v graph.Node) (path []graph.Node, weight float64) {
 		}
 	}
 	ordered.Reverse(path)
-	return path, math.Min(weight, p.dist[p.indexOf[v.ID()]])
+	return path, math.Min(weight, p.dist[p.indexOf[vid]])
 }
 
 // AllShortest is a shortest-path tree created by the DijkstraAllPaths, FloydWarshall
@@ -221,9 +221,9 @@ loop: // These are likely to be rare, so just loop over collisions.
 }
 
 // Weight returns the weight of the minimum path between u and v.
-func (p AllShortest) Weight(u, v graph.Node) float64 {
-	from, fromOK := p.indexOf[u.ID()]
-	to, toOK := p.indexOf[v.ID()]
+func (p AllShortest) Weight(uid, vid int64) float64 {
+	from, fromOK := p.indexOf[uid]
+	to, toOK := p.indexOf[vid]
 	if !fromOK || !toOK {
 		return math.Inf(1)
 	}
@@ -234,11 +234,11 @@ func (p AllShortest) Weight(u, v graph.Node) float64 {
 // one shortest path exists between u and v, a randomly chosen path will be returned and
 // unique is returned false. If a cycle with zero weight exists in the path, it will not
 // be included, but unique will be returned false.
-func (p AllShortest) Between(u, v graph.Node) (path []graph.Node, weight float64, unique bool) {
-	from, fromOK := p.indexOf[u.ID()]
-	to, toOK := p.indexOf[v.ID()]
+func (p AllShortest) Between(uid, vid int64) (path []graph.Node, weight float64, unique bool) {
+	from, fromOK := p.indexOf[uid]
+	to, toOK := p.indexOf[vid]
 	if !fromOK || !toOK || len(p.at(from, to)) == 0 {
-		if u.ID() == v.ID() {
+		if uid == vid {
 			return []graph.Node{p.nodes[from]}, 0, true
 		}
 		return nil, math.Inf(1), false
@@ -290,11 +290,11 @@ func (p AllShortest) Between(u, v graph.Node) (path []graph.Node, weight float64
 
 // AllBetween returns all shortest paths from u to v and the weight of the paths. Paths
 // containing zero-weight cycles are not returned.
-func (p AllShortest) AllBetween(u, v graph.Node) (paths [][]graph.Node, weight float64) {
-	from, fromOK := p.indexOf[u.ID()]
-	to, toOK := p.indexOf[v.ID()]
+func (p AllShortest) AllBetween(uid, vid int64) (paths [][]graph.Node, weight float64) {
+	from, fromOK := p.indexOf[uid]
+	to, toOK := p.indexOf[vid]
 	if !fromOK || !toOK || len(p.at(from, to)) == 0 {
-		if u.ID() == v.ID() {
+		if uid == vid {
 			return [][]graph.Node{{p.nodes[from]}}, 0
 		}
 		return nil, math.Inf(1)
@@ -302,9 +302,9 @@ func (p AllShortest) AllBetween(u, v graph.Node) (paths [][]graph.Node, weight f
 
 	var n graph.Node
 	if p.forward {
-		n = u
+		n = p.nodes[from]
 	} else {
-		n = v
+		n = p.nodes[to]
 	}
 	seen := make([]bool, len(p.nodes))
 	paths = p.allBetween(from, to, seen, []graph.Node{n}, nil)
diff --git a/graph/path/spanning_tree.go b/graph/path/spanning_tree.go
index 79c83638..cee154d3 100644
--- a/graph/path/spanning_tree.go
+++ b/graph/path/spanning_tree.go
@@ -48,8 +48,9 @@ func Prim(dst WeightedBuilder, g graph.WeightedUndirected) float64 {
 	}
 
 	u := nodes[0]
-	for _, v := range g.From(u) {
-		w, ok := g.Weight(u, v)
+	uid := u.ID()
+	for _, v := range g.From(uid) {
+		w, ok := g.Weight(uid, v.ID())
 		if !ok {
 			panic("prim: unexpected invalid weight")
 		}
@@ -59,15 +60,16 @@ func Prim(dst WeightedBuilder, g graph.WeightedUndirected) float64 {
 	var w float64
 	for q.Len() > 0 {
 		e := heap.Pop(q).(simple.WeightedEdge)
-		if e.To() != nil && g.HasEdgeBetween(e.From(), e.To()) {
-			dst.SetWeightedEdge(g.WeightedEdge(e.From(), e.To()))
+		if e.To() != nil && g.HasEdgeBetween(e.From().ID(), e.To().ID()) {
+			dst.SetWeightedEdge(g.WeightedEdge(e.From().ID(), e.To().ID()))
 			w += e.Weight()
 		}
 
 		u = e.From()
-		for _, n := range g.From(u) {
+		uid := u.ID()
+		for _, n := range g.From(uid) {
 			if key, ok := q.key(n); ok {
-				w, ok := g.Weight(u, n)
+				w, ok := g.Weight(uid, n.ID())
 				if !ok {
 					panic("prim: unexpected invalid weight")
 				}
@@ -173,7 +175,7 @@ func Kruskal(dst WeightedBuilder, g UndirectedWeightLister) float64 {
 	for _, e := range edges {
 		if s1, s2 := ds.find(e.From().ID()), ds.find(e.To().ID()); s1 != s2 {
 			ds.union(s1, s2)
-			dst.SetWeightedEdge(g.WeightedEdge(e.From(), e.To()))
+			dst.SetWeightedEdge(g.WeightedEdge(e.From().ID(), e.To().ID()))
 			w += e.Weight()
 		}
 	}
diff --git a/graph/path/spanning_tree_test.go b/graph/path/spanning_tree_test.go
index 007485f3..522579b6 100644
--- a/graph/path/spanning_tree_test.go
+++ b/graph/path/spanning_tree_test.go
@@ -268,7 +268,7 @@ func testMinumumSpanning(mst func(dst WeightedBuilder, g spanningGraph) float64,
 				test.name, len(gotEdges), len(test.treeEdges))
 		}
 		for _, e := range test.treeEdges {
-			w, ok := dst.Weight(e.From(), e.To())
+			w, ok := dst.Weight(e.From().ID(), e.To().ID())
 			if !ok {
 				t.Errorf("spanning tree edge not found in graph for %q: %+v",
 					test.name, e)
diff --git a/graph/path/weight.go b/graph/path/weight.go
index 23b71f90..d5e416e9 100644
--- a/graph/path/weight.go
+++ b/graph/path/weight.go
@@ -12,18 +12,16 @@ import (
 
 // Weighting is a mapping between a pair of nodes and a weight. It follows the
 // semantics of the Weighter interface.
-type Weighting func(x, y graph.Node) (w float64, ok bool)
+type Weighting func(xid, yid int64) (w float64, ok bool)
 
 // UniformCost returns a Weighting that returns an edge cost of 1 for existing
 // edges, zero for node identity and Inf for otherwise absent edges.
 func UniformCost(g graph.Graph) Weighting {
-	return func(x, y graph.Node) (w float64, ok bool) {
-		xid := x.ID()
-		yid := y.ID()
+	return func(xid, yid int64) (w float64, ok bool) {
 		if xid == yid {
 			return 0, true
 		}
-		if e := g.Edge(x, y); e != nil {
+		if e := g.Edge(xid, yid); e != nil {
 			return 1, true
 		}
 		return math.Inf(1), false
diff --git a/graph/simple/dense_directed_matrix.go b/graph/simple/dense_directed_matrix.go
index c393cace..366cee61 100644
--- a/graph/simple/dense_directed_matrix.go
+++ b/graph/simple/dense_directed_matrix.go
@@ -75,8 +75,8 @@ func (g *DirectedMatrix) Node(id int64) graph.Node {
 }
 
 // Has returns whether the node exists within the graph.
-func (g *DirectedMatrix) Has(n graph.Node) bool {
-	return g.has(n.ID())
+func (g *DirectedMatrix) Has(id int64) bool {
+	return g.has(id)
 }
 
 func (g *DirectedMatrix) has(id int64) bool {
@@ -117,8 +117,7 @@ func (g *DirectedMatrix) Edges() []graph.Edge {
 }
 
 // From returns all nodes in g that can be reached directly from n.
-func (g *DirectedMatrix) From(n graph.Node) []graph.Node {
-	id := n.ID()
+func (g *DirectedMatrix) From(id int64) []graph.Node {
 	if !g.has(id) {
 		return nil
 	}
@@ -137,8 +136,7 @@ func (g *DirectedMatrix) From(n graph.Node) []graph.Node {
 }
 
 // To returns all nodes in g that can reach directly to n.
-func (g *DirectedMatrix) To(n graph.Node) []graph.Node {
-	id := n.ID()
+func (g *DirectedMatrix) To(id int64) []graph.Node {
 	if !g.has(id) {
 		return nil
 	}
@@ -158,12 +156,10 @@ func (g *DirectedMatrix) To(n graph.Node) []graph.Node {
 
 // HasEdgeBetween returns whether an edge exists between nodes x and y without
 // considering direction.
-func (g *DirectedMatrix) HasEdgeBetween(x, y graph.Node) bool {
-	xid := x.ID()
+func (g *DirectedMatrix) HasEdgeBetween(xid, yid int64) bool {
 	if !g.has(xid) {
 		return false
 	}
-	yid := y.ID()
 	if !g.has(yid) {
 		return false
 	}
@@ -173,27 +169,25 @@ func (g *DirectedMatrix) HasEdgeBetween(x, y graph.Node) bool {
 
 // Edge returns the edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g *DirectedMatrix) Edge(u, v graph.Node) graph.Edge {
-	return g.WeightedEdge(u, v)
+func (g *DirectedMatrix) Edge(uid, vid int64) graph.Edge {
+	return g.WeightedEdge(uid, vid)
 }
 
 // WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g *DirectedMatrix) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
-	if g.HasEdgeFromTo(u, v) {
-		// x.ID() and y.ID() are not greater than maximum int by this point.
-		return WeightedEdge{F: g.Node(u.ID()), T: g.Node(v.ID()), W: g.mat.At(int(u.ID()), int(v.ID()))}
+func (g *DirectedMatrix) WeightedEdge(uid, vid int64) graph.WeightedEdge {
+	if g.HasEdgeFromTo(uid, vid) {
+		// xid and yid are not greater than maximum int by this point.
+		return WeightedEdge{F: g.Node(uid), T: g.Node(vid), W: g.mat.At(int(uid), int(vid))}
 	}
 	return nil
 }
 
 // HasEdgeFromTo returns whether an edge exists in the graph from u to v.
-func (g *DirectedMatrix) HasEdgeFromTo(u, v graph.Node) bool {
-	uid := u.ID()
+func (g *DirectedMatrix) HasEdgeFromTo(uid, vid int64) bool {
 	if !g.has(uid) {
 		return false
 	}
-	vid := v.ID()
 	if !g.has(vid) {
 		return false
 	}
@@ -205,9 +199,7 @@ func (g *DirectedMatrix) HasEdgeFromTo(u, v graph.Node) bool {
 // If x and y are the same node or there is no joining edge between the two nodes the weight
 // value returned is either the graph's absent or self value. Weight returns true if an edge
 // exists between x and y or if x and y have the same ID, false otherwise.
-func (g *DirectedMatrix) Weight(x, y graph.Node) (w float64, ok bool) {
-	xid := x.ID()
-	yid := y.ID()
+func (g *DirectedMatrix) Weight(xid, yid int64) (w float64, ok bool) {
 	if xid == yid {
 		return g.self, true
 	}
@@ -262,8 +254,7 @@ func (g *DirectedMatrix) RemoveEdge(e graph.Edge) {
 }
 
 // Degree returns the in+out degree of n in g.
-func (g *DirectedMatrix) Degree(n graph.Node) int {
-	id := n.ID()
+func (g *DirectedMatrix) Degree(id int64) int {
 	if !g.has(id) {
 		return 0
 	}
diff --git a/graph/simple/dense_undirected_matrix.go b/graph/simple/dense_undirected_matrix.go
index 9276d9e6..97142ab1 100644
--- a/graph/simple/dense_undirected_matrix.go
+++ b/graph/simple/dense_undirected_matrix.go
@@ -75,8 +75,8 @@ func (g *UndirectedMatrix) Node(id int64) graph.Node {
 }
 
 // Has returns whether the node exists within the graph.
-func (g *UndirectedMatrix) Has(n graph.Node) bool {
-	return g.has(n.ID())
+func (g *UndirectedMatrix) Has(id int64) bool {
+	return g.has(id)
 }
 
 func (g *UndirectedMatrix) has(id int64) bool {
@@ -114,8 +114,7 @@ func (g *UndirectedMatrix) Edges() []graph.Edge {
 }
 
 // From returns all nodes in g that can be reached directly from n.
-func (g *UndirectedMatrix) From(n graph.Node) []graph.Node {
-	id := n.ID()
+func (g *UndirectedMatrix) From(id int64) []graph.Node {
 	if !g.has(id) {
 		return nil
 	}
@@ -134,12 +133,10 @@ func (g *UndirectedMatrix) From(n graph.Node) []graph.Node {
 }
 
 // HasEdgeBetween returns whether an edge exists between nodes x and y.
-func (g *UndirectedMatrix) HasEdgeBetween(u, v graph.Node) bool {
-	uid := u.ID()
+func (g *UndirectedMatrix) HasEdgeBetween(uid, vid int64) bool {
 	if !g.has(uid) {
 		return false
 	}
-	vid := v.ID()
 	if !g.has(vid) {
 		return false
 	}
@@ -149,26 +146,26 @@ func (g *UndirectedMatrix) HasEdgeBetween(u, v graph.Node) bool {
 
 // Edge returns the edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g *UndirectedMatrix) Edge(u, v graph.Node) graph.Edge {
-	return g.WeightedEdgeBetween(u, v)
+func (g *UndirectedMatrix) Edge(uid, vid int64) graph.Edge {
+	return g.WeightedEdgeBetween(uid, vid)
 }
 
 // WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g *UndirectedMatrix) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
-	return g.WeightedEdgeBetween(u, v)
+func (g *UndirectedMatrix) WeightedEdge(uid, vid int64) graph.WeightedEdge {
+	return g.WeightedEdgeBetween(uid, vid)
 }
 
 // EdgeBetween returns the edge between nodes x and y.
-func (g *UndirectedMatrix) EdgeBetween(u, v graph.Node) graph.Edge {
-	return g.WeightedEdgeBetween(u, v)
+func (g *UndirectedMatrix) EdgeBetween(uid, vid int64) graph.Edge {
+	return g.WeightedEdgeBetween(uid, vid)
 }
 
 // WeightedEdgeBetween returns the weighted edge between nodes x and y.
-func (g *UndirectedMatrix) WeightedEdgeBetween(u, v graph.Node) graph.WeightedEdge {
-	if g.HasEdgeBetween(u, v) {
-		// u.ID() and v.ID() are not greater than maximum int by this point.
-		return WeightedEdge{F: g.Node(u.ID()), T: g.Node(v.ID()), W: g.mat.At(int(u.ID()), int(v.ID()))}
+func (g *UndirectedMatrix) WeightedEdgeBetween(uid, vid int64) graph.WeightedEdge {
+	if g.HasEdgeBetween(uid, vid) {
+		// uid and vid are not greater than maximum int by this point.
+		return WeightedEdge{F: g.Node(uid), T: g.Node(vid), W: g.mat.At(int(uid), int(vid))}
 	}
 	return nil
 }
@@ -177,9 +174,7 @@ func (g *UndirectedMatrix) WeightedEdgeBetween(u, v graph.Node) graph.WeightedEd
 // If x and y are the same node or there is no joining edge between the two nodes the weight
 // value returned is either the graph's absent or self value. Weight returns true if an edge
 // exists between x and y or if x and y have the same ID, false otherwise.
-func (g *UndirectedMatrix) Weight(x, y graph.Node) (w float64, ok bool) {
-	xid := x.ID()
-	yid := y.ID()
+func (g *UndirectedMatrix) Weight(xid, yid int64) (w float64, ok bool) {
 	if xid == yid {
 		return g.self, true
 	}
@@ -234,8 +229,7 @@ func (g *UndirectedMatrix) RemoveEdge(e graph.Edge) {
 }
 
 // Degree returns the degree of n in g.
-func (g *UndirectedMatrix) Degree(n graph.Node) int {
-	id := n.ID()
+func (g *UndirectedMatrix) Degree(id int64) int {
 	if !g.has(id) {
 		return 0
 	}
diff --git a/graph/simple/densegraph_test.go b/graph/simple/densegraph_test.go
index 51cba241..595b4e9a 100644
--- a/graph/simple/densegraph_test.go
+++ b/graph/simple/densegraph_test.go
@@ -34,17 +34,17 @@ func TestBasicDenseImpassable(t *testing.T) {
 	}
 
 	for i := 0; i < 5; i++ {
-		if !dg.Has(Node(i)) {
+		if !dg.Has(int64(i)) {
 			t.Errorf("Node that should exist doesn't: %d", i)
 		}
 
-		if degree := dg.Degree(Node(i)); degree != 0 {
+		if degree := dg.Degree(int64(i)); degree != 0 {
 			t.Errorf("Node in impassable graph has a neighbor. Node: %d Degree: %d", i, degree)
 		}
 	}
 
 	for i := 5; i < 10; i++ {
-		if dg.Has(Node(i)) {
+		if dg.Has(int64(i)) {
 			t.Errorf("Node exists that shouldn't: %d", i)
 		}
 	}
@@ -57,17 +57,17 @@ func TestBasicDensePassable(t *testing.T) {
 	}
 
 	for i := 0; i < 5; i++ {
-		if !dg.Has(Node(i)) {
+		if !dg.Has(int64(i)) {
 			t.Errorf("Node that should exist doesn't: %d", i)
 		}
 
-		if degree := dg.Degree(Node(i)); degree != 4 {
+		if degree := dg.Degree(int64(i)); degree != 4 {
 			t.Errorf("Node in passable graph missing neighbors. Node: %d Degree: %d", i, degree)
 		}
 	}
 
 	for i := 5; i < 10; i++ {
-		if dg.Has(Node(i)) {
+		if dg.Has(int64(i)) {
 			t.Errorf("Node exists that shouldn't: %d", i)
 		}
 	}
@@ -77,29 +77,29 @@ func TestDirectedDenseAddRemove(t *testing.T) {
 	dg := NewDirectedMatrix(10, math.Inf(1), 0, math.Inf(1))
 	dg.SetWeightedEdge(WeightedEdge{F: Node(0), T: Node(2), W: 1})
 
-	if neighbors := dg.From(Node(0)); len(neighbors) != 1 || neighbors[0].ID() != 2 ||
-		dg.Edge(Node(0), Node(2)) == nil {
+	if neighbors := dg.From(int64(0)); len(neighbors) != 1 || neighbors[0].ID() != 2 ||
+		dg.Edge(int64(0), int64(2)) == nil {
 		t.Errorf("Adding edge didn't create successor")
 	}
 
 	dg.RemoveEdge(Edge{F: Node(0), T: Node(2)})
 
-	if neighbors := dg.From(Node(0)); len(neighbors) != 0 || dg.Edge(Node(0), Node(2)) != nil {
+	if neighbors := dg.From(int64(0)); len(neighbors) != 0 || dg.Edge(int64(0), int64(2)) != nil {
 		t.Errorf("Removing edge didn't properly remove successor")
 	}
 
-	if neighbors := dg.To(Node(2)); len(neighbors) != 0 || dg.Edge(Node(0), Node(2)) != nil {
+	if neighbors := dg.To(int64(2)); len(neighbors) != 0 || dg.Edge(int64(0), int64(2)) != nil {
 		t.Errorf("Removing directed edge wrongly kept predecessor")
 	}
 
 	dg.SetWeightedEdge(WeightedEdge{F: Node(0), T: Node(2), W: 2})
 	// I figure we've torture tested From/To at this point
 	// so we'll just use the bool functions now
-	if dg.Edge(Node(0), Node(2)) == nil {
+	if dg.Edge(int64(0), int64(2)) == nil {
 		t.Fatal("Adding directed edge didn't change successor back")
 	}
-	c1, _ := dg.Weight(Node(2), Node(0))
-	c2, _ := dg.Weight(Node(0), Node(2))
+	c1, _ := dg.Weight(int64(2), int64(0))
+	c2, _ := dg.Weight(int64(0), int64(2))
 	if c1 == c2 {
 		t.Error("Adding directed edge affected cost in undirected manner")
 	}
@@ -109,13 +109,13 @@ func TestUndirectedDenseAddRemove(t *testing.T) {
 	dg := NewUndirectedMatrix(10, math.Inf(1), 0, math.Inf(1))
 	dg.SetEdge(Edge{F: Node(0), T: Node(2)})
 
-	if neighbors := dg.From(Node(0)); len(neighbors) != 1 || neighbors[0].ID() != 2 ||
-		dg.EdgeBetween(Node(0), Node(2)) == nil {
+	if neighbors := dg.From(int64(0)); len(neighbors) != 1 || neighbors[0].ID() != 2 ||
+		dg.EdgeBetween(int64(0), int64(2)) == nil {
 		t.Errorf("Couldn't add neighbor")
 	}
 
-	if neighbors := dg.From(Node(2)); len(neighbors) != 1 || neighbors[0].ID() != 0 ||
-		dg.EdgeBetween(Node(2), Node(0)) == nil {
+	if neighbors := dg.From(int64(2)); len(neighbors) != 1 || neighbors[0].ID() != 0 ||
+		dg.EdgeBetween(int64(2), int64(0)) == nil {
 		t.Errorf("Adding an undirected neighbor didn't add it reciprocally")
 	}
 }
diff --git a/graph/simple/directed.go b/graph/simple/directed.go
index 06500f17..d2a58f31 100644
--- a/graph/simple/directed.go
+++ b/graph/simple/directed.go
@@ -94,10 +94,10 @@ func (g *DirectedGraph) SetEdge(e graph.Edge) {
 		panic("simple: adding self edge")
 	}
 
-	if !g.Has(from) {
+	if !g.Has(fid) {
 		g.AddNode(from)
 	}
-	if !g.Has(to) {
+	if !g.Has(tid) {
 		g.AddNode(to)
 	}
 
@@ -126,8 +126,8 @@ func (g *DirectedGraph) Node(id int64) graph.Node {
 }
 
 // Has returns whether the node exists within the graph.
-func (g *DirectedGraph) Has(n graph.Node) bool {
-	_, ok := g.nodes[n.ID()]
+func (g *DirectedGraph) Has(id int64) bool {
+	_, ok := g.nodes[id]
 	return ok
 }
 
@@ -157,30 +157,30 @@ func (g *DirectedGraph) Edges() []graph.Edge {
 }
 
 // From returns all nodes in g that can be reached directly from n.
-func (g *DirectedGraph) From(n graph.Node) []graph.Node {
-	if _, ok := g.from[n.ID()]; !ok {
+func (g *DirectedGraph) From(id int64) []graph.Node {
+	if _, ok := g.from[id]; !ok {
 		return nil
 	}
 
-	from := make([]graph.Node, len(g.from[n.ID()]))
+	from := make([]graph.Node, len(g.from[id]))
 	i := 0
-	for id := range g.from[n.ID()] {
-		from[i] = g.nodes[id]
+	for vid := range g.from[id] {
+		from[i] = g.nodes[vid]
 		i++
 	}
 	return from
 }
 
 // To returns all nodes in g that can reach directly to n.
-func (g *DirectedGraph) To(n graph.Node) []graph.Node {
-	if _, ok := g.from[n.ID()]; !ok {
+func (g *DirectedGraph) To(id int64) []graph.Node {
+	if _, ok := g.from[id]; !ok {
 		return nil
 	}
 
-	to := make([]graph.Node, len(g.to[n.ID()]))
+	to := make([]graph.Node, len(g.to[id]))
 	i := 0
-	for id := range g.to[n.ID()] {
-		to[i] = g.nodes[id]
+	for uid := range g.to[id] {
+		to[i] = g.nodes[uid]
 		i++
 	}
 	return to
@@ -188,9 +188,7 @@ func (g *DirectedGraph) To(n graph.Node) []graph.Node {
 
 // HasEdgeBetween returns whether an edge exists between nodes x and y without
 // considering direction.
-func (g *DirectedGraph) HasEdgeBetween(x, y graph.Node) bool {
-	xid := x.ID()
-	yid := y.ID()
+func (g *DirectedGraph) HasEdgeBetween(xid, yid int64) bool {
 	if _, ok := g.from[xid][yid]; ok {
 		return true
 	}
@@ -200,8 +198,8 @@ func (g *DirectedGraph) HasEdgeBetween(x, y graph.Node) bool {
 
 // Edge returns the edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g *DirectedGraph) Edge(u, v graph.Node) graph.Edge {
-	edge, ok := g.from[u.ID()][v.ID()]
+func (g *DirectedGraph) Edge(uid, vid int64) graph.Edge {
+	edge, ok := g.from[uid][vid]
 	if !ok {
 		return nil
 	}
@@ -209,17 +207,17 @@ func (g *DirectedGraph) Edge(u, v graph.Node) graph.Edge {
 }
 
 // HasEdgeFromTo returns whether an edge exists in the graph from u to v.
-func (g *DirectedGraph) HasEdgeFromTo(u, v graph.Node) bool {
-	if _, ok := g.from[u.ID()][v.ID()]; !ok {
+func (g *DirectedGraph) HasEdgeFromTo(uid, vid int64) bool {
+	if _, ok := g.from[uid][vid]; !ok {
 		return false
 	}
 	return true
 }
 
 // Degree returns the in+out degree of n in g.
-func (g *DirectedGraph) Degree(n graph.Node) int {
-	if _, ok := g.nodes[n.ID()]; !ok {
+func (g *DirectedGraph) Degree(id int64) int {
+	if _, ok := g.nodes[id]; !ok {
 		return 0
 	}
-	return len(g.from[n.ID()]) + len(g.to[n.ID()])
+	return len(g.from[id]) + len(g.to[id])
 }
diff --git a/graph/simple/directed_test.go b/graph/simple/directed_test.go
index 45bc5b1c..0de3fbd3 100644
--- a/graph/simple/directed_test.go
+++ b/graph/simple/directed_test.go
@@ -21,7 +21,7 @@ var (
 func TestEdgeOvercounting(t *testing.T) {
 	g := generateDummyGraph()
 
-	if neigh := g.From(Node(Node(2))); len(neigh) != 2 {
+	if neigh := g.From(int64(2)); len(neigh) != 2 {
 		t.Errorf("Node 2 has incorrect number of neighbors got neighbors %v (count %d), expected 2 neighbors {0,1}", neigh, len(neigh))
 	}
 }
diff --git a/graph/simple/undirected.go b/graph/simple/undirected.go
index 818e506b..a43fcf16 100644
--- a/graph/simple/undirected.go
+++ b/graph/simple/undirected.go
@@ -86,10 +86,10 @@ func (g *UndirectedGraph) SetEdge(e graph.Edge) {
 		panic("simple: adding self edge")
 	}
 
-	if !g.Has(from) {
+	if !g.Has(fid) {
 		g.AddNode(from)
 	}
-	if !g.Has(to) {
+	if !g.Has(tid) {
 		g.AddNode(to)
 	}
 
@@ -118,8 +118,8 @@ func (g *UndirectedGraph) Node(id int64) graph.Node {
 }
 
 // Has returns whether the node exists within the graph.
-func (g *UndirectedGraph) Has(n graph.Node) bool {
-	_, ok := g.nodes[n.ID()]
+func (g *UndirectedGraph) Has(id int64) bool {
+	_, ok := g.nodes[id]
 	return ok
 }
 
@@ -160,14 +160,14 @@ func (g *UndirectedGraph) Edges() []graph.Edge {
 }
 
 // From returns all nodes in g that can be reached directly from n.
-func (g *UndirectedGraph) From(n graph.Node) []graph.Node {
-	if !g.Has(n) {
+func (g *UndirectedGraph) From(id int64) []graph.Node {
+	if !g.Has(id) {
 		return nil
 	}
 
-	nodes := make([]graph.Node, len(g.edges[n.ID()]))
+	nodes := make([]graph.Node, len(g.edges[id]))
 	i := 0
-	for from := range g.edges[n.ID()] {
+	for from := range g.edges[id] {
 		nodes[i] = g.nodes[from]
 		i++
 	}
@@ -175,20 +175,20 @@ func (g *UndirectedGraph) From(n graph.Node) []graph.Node {
 }
 
 // HasEdgeBetween returns whether an edge exists between nodes x and y.
-func (g *UndirectedGraph) HasEdgeBetween(x, y graph.Node) bool {
-	_, ok := g.edges[x.ID()][y.ID()]
+func (g *UndirectedGraph) HasEdgeBetween(xid, yid int64) bool {
+	_, ok := g.edges[xid][yid]
 	return ok
 }
 
 // Edge returns the edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g *UndirectedGraph) Edge(u, v graph.Node) graph.Edge {
-	return g.EdgeBetween(u, v)
+func (g *UndirectedGraph) Edge(uid, vid int64) graph.Edge {
+	return g.EdgeBetween(uid, vid)
 }
 
 // EdgeBetween returns the edge between nodes x and y.
-func (g *UndirectedGraph) EdgeBetween(x, y graph.Node) graph.Edge {
-	edge, ok := g.edges[x.ID()][y.ID()]
+func (g *UndirectedGraph) EdgeBetween(xid, yid int64) graph.Edge {
+	edge, ok := g.edges[xid][yid]
 	if !ok {
 		return nil
 	}
@@ -196,9 +196,9 @@ func (g *UndirectedGraph) EdgeBetween(x, y graph.Node) graph.Edge {
 }
 
 // Degree returns the degree of n in g.
-func (g *UndirectedGraph) Degree(n graph.Node) int {
-	if _, ok := g.nodes[n.ID()]; !ok {
+func (g *UndirectedGraph) Degree(id int64) int {
+	if _, ok := g.nodes[id]; !ok {
 		return 0
 	}
-	return len(g.edges[n.ID()])
+	return len(g.edges[id])
 }
diff --git a/graph/simple/undirected_test.go b/graph/simple/undirected_test.go
index 63719aa0..9251bfe7 100644
--- a/graph/simple/undirected_test.go
+++ b/graph/simple/undirected_test.go
@@ -37,7 +37,7 @@ func TestMaxID(t *testing.T) {
 	delete(nodes, Node(2))
 	n := g.NewNode()
 	g.AddNode(n)
-	if !g.Has(n) {
+	if !g.Has(n.ID()) {
 		t.Error("added node does not exist in graph")
 	}
 	if _, exists := nodes[n]; exists {
diff --git a/graph/simple/weighted_directed.go b/graph/simple/weighted_directed.go
index 93767930..004cb852 100644
--- a/graph/simple/weighted_directed.go
+++ b/graph/simple/weighted_directed.go
@@ -100,10 +100,10 @@ func (g *WeightedDirectedGraph) SetWeightedEdge(e graph.WeightedEdge) {
 		panic("simple: adding self edge")
 	}
 
-	if !g.Has(from) {
+	if !g.Has(fid) {
 		g.AddNode(from)
 	}
-	if !g.Has(to) {
+	if !g.Has(tid) {
 		g.AddNode(to)
 	}
 
@@ -132,8 +132,8 @@ func (g *WeightedDirectedGraph) Node(id int64) graph.Node {
 }
 
 // Has returns whether the node exists within the graph.
-func (g *WeightedDirectedGraph) Has(n graph.Node) bool {
-	_, ok := g.nodes[n.ID()]
+func (g *WeightedDirectedGraph) Has(id int64) bool {
+	_, ok := g.nodes[id]
 	return ok
 }
 
@@ -174,30 +174,30 @@ func (g *WeightedDirectedGraph) WeightedEdges() []graph.WeightedEdge {
 }
 
 // From returns all nodes in g that can be reached directly from n.
-func (g *WeightedDirectedGraph) From(n graph.Node) []graph.Node {
-	if _, ok := g.from[n.ID()]; !ok {
+func (g *WeightedDirectedGraph) From(id int64) []graph.Node {
+	if _, ok := g.from[id]; !ok {
 		return nil
 	}
 
-	from := make([]graph.Node, len(g.from[n.ID()]))
+	from := make([]graph.Node, len(g.from[id]))
 	i := 0
-	for id := range g.from[n.ID()] {
-		from[i] = g.nodes[id]
+	for vid := range g.from[id] {
+		from[i] = g.nodes[vid]
 		i++
 	}
 	return from
 }
 
 // To returns all nodes in g that can reach directly to n.
-func (g *WeightedDirectedGraph) To(n graph.Node) []graph.Node {
-	if _, ok := g.from[n.ID()]; !ok {
+func (g *WeightedDirectedGraph) To(id int64) []graph.Node {
+	if _, ok := g.from[id]; !ok {
 		return nil
 	}
 
-	to := make([]graph.Node, len(g.to[n.ID()]))
+	to := make([]graph.Node, len(g.to[id]))
 	i := 0
-	for id := range g.to[n.ID()] {
-		to[i] = g.nodes[id]
+	for uid := range g.to[id] {
+		to[i] = g.nodes[uid]
 		i++
 	}
 	return to
@@ -205,9 +205,7 @@ func (g *WeightedDirectedGraph) To(n graph.Node) []graph.Node {
 
 // HasEdgeBetween returns whether an edge exists between nodes x and y without
 // considering direction.
-func (g *WeightedDirectedGraph) HasEdgeBetween(x, y graph.Node) bool {
-	xid := x.ID()
-	yid := y.ID()
+func (g *WeightedDirectedGraph) HasEdgeBetween(xid, yid int64) bool {
 	if _, ok := g.from[xid][yid]; ok {
 		return true
 	}
@@ -217,14 +215,14 @@ func (g *WeightedDirectedGraph) HasEdgeBetween(x, y graph.Node) bool {
 
 // Edge returns the edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g *WeightedDirectedGraph) Edge(u, v graph.Node) graph.Edge {
-	return g.WeightedEdge(u, v)
+func (g *WeightedDirectedGraph) Edge(uid, vid int64) graph.Edge {
+	return g.WeightedEdge(uid, vid)
 }
 
 // WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g *WeightedDirectedGraph) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
-	edge, ok := g.from[u.ID()][v.ID()]
+func (g *WeightedDirectedGraph) WeightedEdge(uid, vid int64) graph.WeightedEdge {
+	edge, ok := g.from[uid][vid]
 	if !ok {
 		return nil
 	}
@@ -232,8 +230,8 @@ func (g *WeightedDirectedGraph) WeightedEdge(u, v graph.Node) graph.WeightedEdge
 }
 
 // HasEdgeFromTo returns whether an edge exists in the graph from u to v.
-func (g *WeightedDirectedGraph) HasEdgeFromTo(u, v graph.Node) bool {
-	if _, ok := g.from[u.ID()][v.ID()]; !ok {
+func (g *WeightedDirectedGraph) HasEdgeFromTo(uid, vid int64) bool {
+	if _, ok := g.from[uid][vid]; !ok {
 		return false
 	}
 	return true
@@ -243,9 +241,7 @@ func (g *WeightedDirectedGraph) HasEdgeFromTo(u, v graph.Node) bool {
 // If x and y are the same node or there is no joining edge between the two nodes the weight
 // value returned is either the graph's absent or self value. Weight returns true if an edge
 // exists between x and y or if x and y have the same ID, false otherwise.
-func (g *WeightedDirectedGraph) Weight(x, y graph.Node) (w float64, ok bool) {
-	xid := x.ID()
-	yid := y.ID()
+func (g *WeightedDirectedGraph) Weight(xid, yid int64) (w float64, ok bool) {
 	if xid == yid {
 		return g.self, true
 	}
@@ -258,9 +254,9 @@ func (g *WeightedDirectedGraph) Weight(x, y graph.Node) (w float64, ok bool) {
 }
 
 // Degree returns the in+out degree of n in g.
-func (g *WeightedDirectedGraph) Degree(n graph.Node) int {
-	if _, ok := g.nodes[n.ID()]; !ok {
+func (g *WeightedDirectedGraph) Degree(id int64) int {
+	if _, ok := g.nodes[id]; !ok {
 		return 0
 	}
-	return len(g.from[n.ID()]) + len(g.to[n.ID()])
+	return len(g.from[id]) + len(g.to[id])
 }
diff --git a/graph/simple/weighted_directed_test.go b/graph/simple/weighted_directed_test.go
index e7d210d1..18c87414 100644
--- a/graph/simple/weighted_directed_test.go
+++ b/graph/simple/weighted_directed_test.go
@@ -23,7 +23,7 @@ var (
 func TestWeightedEdgeOvercounting(t *testing.T) {
 	g := generateDummyGraph()
 
-	if neigh := g.From(Node(Node(2))); len(neigh) != 2 {
+	if neigh := g.From(int64(2)); len(neigh) != 2 {
 		t.Errorf("Node 2 has incorrect number of neighbors got neighbors %v (count %d), expected 2 neighbors {0,1}", neigh, len(neigh))
 	}
 }
diff --git a/graph/simple/weighted_undirected.go b/graph/simple/weighted_undirected.go
index 78fe81f6..9bf02f28 100644
--- a/graph/simple/weighted_undirected.go
+++ b/graph/simple/weighted_undirected.go
@@ -92,10 +92,10 @@ func (g *WeightedUndirectedGraph) SetWeightedEdge(e graph.WeightedEdge) {
 		panic("simple: adding self edge")
 	}
 
-	if !g.Has(from) {
+	if !g.Has(fid) {
 		g.AddNode(from)
 	}
-	if !g.Has(to) {
+	if !g.Has(tid) {
 		g.AddNode(to)
 	}
 
@@ -124,8 +124,8 @@ func (g *WeightedUndirectedGraph) Node(id int64) graph.Node {
 }
 
 // Has returns whether the node exists within the graph.
-func (g *WeightedUndirectedGraph) Has(n graph.Node) bool {
-	_, ok := g.nodes[n.ID()]
+func (g *WeightedUndirectedGraph) Has(id int64) bool {
+	_, ok := g.nodes[id]
 	return ok
 }
 
@@ -185,14 +185,14 @@ func (g *WeightedUndirectedGraph) WeightedEdges() []graph.WeightedEdge {
 }
 
 // From returns all nodes in g that can be reached directly from n.
-func (g *WeightedUndirectedGraph) From(n graph.Node) []graph.Node {
-	if !g.Has(n) {
+func (g *WeightedUndirectedGraph) From(id int64) []graph.Node {
+	if !g.Has(id) {
 		return nil
 	}
 
-	nodes := make([]graph.Node, len(g.edges[n.ID()]))
+	nodes := make([]graph.Node, len(g.edges[id]))
 	i := 0
-	for from := range g.edges[n.ID()] {
+	for from := range g.edges[id] {
 		nodes[i] = g.nodes[from]
 		i++
 	}
@@ -200,31 +200,31 @@ func (g *WeightedUndirectedGraph) From(n graph.Node) []graph.Node {
 }
 
 // HasEdgeBetween returns whether an edge exists between nodes x and y.
-func (g *WeightedUndirectedGraph) HasEdgeBetween(x, y graph.Node) bool {
-	_, ok := g.edges[x.ID()][y.ID()]
+func (g *WeightedUndirectedGraph) HasEdgeBetween(xid, yid int64) bool {
+	_, ok := g.edges[xid][yid]
 	return ok
 }
 
 // Edge returns the edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g *WeightedUndirectedGraph) Edge(u, v graph.Node) graph.Edge {
-	return g.WeightedEdgeBetween(u, v)
+func (g *WeightedUndirectedGraph) Edge(uid, vid int64) graph.Edge {
+	return g.WeightedEdgeBetween(uid, vid)
 }
 
 // WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
-func (g *WeightedUndirectedGraph) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
-	return g.WeightedEdgeBetween(u, v)
+func (g *WeightedUndirectedGraph) WeightedEdge(uid, vid int64) graph.WeightedEdge {
+	return g.WeightedEdgeBetween(uid, vid)
 }
 
 // EdgeBetween returns the edge between nodes x and y.
-func (g *WeightedUndirectedGraph) EdgeBetween(x, y graph.Node) graph.Edge {
-	return g.WeightedEdgeBetween(x, y)
+func (g *WeightedUndirectedGraph) EdgeBetween(xid, yid int64) graph.Edge {
+	return g.WeightedEdgeBetween(xid, yid)
 }
 
 // WeightedEdgeBetween returns the weighted edge between nodes x and y.
-func (g *WeightedUndirectedGraph) WeightedEdgeBetween(x, y graph.Node) graph.WeightedEdge {
-	edge, ok := g.edges[x.ID()][y.ID()]
+func (g *WeightedUndirectedGraph) WeightedEdgeBetween(xid, yid int64) graph.WeightedEdge {
+	edge, ok := g.edges[xid][yid]
 	if !ok {
 		return nil
 	}
@@ -235,9 +235,7 @@ func (g *WeightedUndirectedGraph) WeightedEdgeBetween(x, y graph.Node) graph.Wei
 // If x and y are the same node or there is no joining edge between the two nodes the weight
 // value returned is either the graph's absent or self value. Weight returns true if an edge
 // exists between x and y or if x and y have the same ID, false otherwise.
-func (g *WeightedUndirectedGraph) Weight(x, y graph.Node) (w float64, ok bool) {
-	xid := x.ID()
-	yid := y.ID()
+func (g *WeightedUndirectedGraph) Weight(xid, yid int64) (w float64, ok bool) {
 	if xid == yid {
 		return g.self, true
 	}
@@ -250,9 +248,9 @@ func (g *WeightedUndirectedGraph) Weight(x, y graph.Node) (w float64, ok bool) {
 }
 
 // Degree returns the degree of n in g.
-func (g *WeightedUndirectedGraph) Degree(n graph.Node) int {
-	if _, ok := g.nodes[n.ID()]; !ok {
+func (g *WeightedUndirectedGraph) Degree(id int64) int {
+	if _, ok := g.nodes[id]; !ok {
 		return 0
 	}
-	return len(g.edges[n.ID()])
+	return len(g.edges[id])
 }
diff --git a/graph/simple/weighted_undirected_test.go b/graph/simple/weighted_undirected_test.go
index a885821e..5111fb16 100644
--- a/graph/simple/weighted_undirected_test.go
+++ b/graph/simple/weighted_undirected_test.go
@@ -39,7 +39,7 @@ func TestWeightedMaxID(t *testing.T) {
 	delete(nodes, Node(2))
 	n := g.NewNode()
 	g.AddNode(n)
-	if !g.Has(n) {
+	if !g.Has(n.ID()) {
 		t.Error("added node does not exist in graph")
 	}
 	if _, exists := nodes[n]; exists {
diff --git a/graph/topo/2sat_example_test.go b/graph/topo/2sat_example_test.go
index 4b89093a..e7fc784b 100644
--- a/graph/topo/2sat_example_test.go
+++ b/graph/topo/2sat_example_test.go
@@ -123,7 +123,7 @@ func twoSat(r io.Reader) (state map[string]bool, ok bool) {
 		// Check for tautology.
 		if variables[0].negated().ID() == variables[1].ID() {
 			for _, v := range variables {
-				if !g.Has(v) {
+				if !g.Has(v.ID()) {
 					g.AddNode(v)
 				}
 			}
diff --git a/graph/topo/bron_kerbosch.go b/graph/topo/bron_kerbosch.go
index ced15f15..c602b13a 100644
--- a/graph/topo/bron_kerbosch.go
+++ b/graph/topo/bron_kerbosch.go
@@ -60,9 +60,10 @@ func degeneracyOrdering(g graph.Undirected) (l []graph.Node, s []int) {
 		neighbours = make(map[int64][]graph.Node)
 	)
 	for _, n := range nodes {
-		adj := g.From(n)
-		neighbours[n.ID()] = adj
-		dv[n.ID()] = len(adj)
+		id := n.ID()
+		adj := g.From(id)
+		neighbours[id] = adj
+		dv[id] = len(adj)
 		if len(adj) > maxDegree {
 			maxDegree = len(adj)
 		}
@@ -146,7 +147,7 @@ func BronKerbosch(g graph.Undirected) [][]graph.Node {
 	order, _ := degeneracyOrdering(g)
 	ordered.Reverse(order)
 	for _, v := range order {
-		neighbours := g.From(v)
+		neighbours := g.From(v.ID())
 		nv := make(set.Nodes, len(neighbours))
 		for _, n := range neighbours {
 			nv.Add(n)
@@ -175,7 +176,8 @@ func (bk *bronKerbosch) maximalCliquePivot(g graph.Undirected, r []graph.Node, p
 		if nu.Has(v) {
 			continue
 		}
-		neighbours := g.From(v)
+		vid := v.ID()
+		neighbours := g.From(vid)
 		nv := make(set.Nodes, len(neighbours))
 		for _, n := range neighbours {
 			nv.Add(n)
@@ -183,7 +185,7 @@ func (bk *bronKerbosch) maximalCliquePivot(g graph.Undirected, r []graph.Node, p
 
 		var found bool
 		for _, n := range r {
-			if n.ID() == v.ID() {
+			if n.ID() == vid {
 				found = true
 				break
 			}
@@ -205,10 +207,10 @@ func (*bronKerbosch) choosePivotFrom(g graph.Undirected, p, x set.Nodes) (neighb
 	// compile time option.
 	if !tomitaTanakaTakahashi {
 		for _, n := range p {
-			return g.From(n)
+			return g.From(n.ID())
 		}
 		for _, n := range x {
-			return g.From(n)
+			return g.From(n.ID())
 		}
 		panic("bronKerbosch: empty set")
 	}
@@ -220,7 +222,7 @@ func (*bronKerbosch) choosePivotFrom(g graph.Undirected, p, x set.Nodes) (neighb
 	maxNeighbors := func(s set.Nodes) {
 	outer:
 		for _, u := range s {
-			nb := g.From(u)
+			nb := g.From(u.ID())
 			c := len(nb)
 			if c <= max {
 				continue
diff --git a/graph/topo/bron_kerbosch_test.go b/graph/topo/bron_kerbosch_test.go
index e04e06dc..93d50167 100644
--- a/graph/topo/bron_kerbosch_test.go
+++ b/graph/topo/bron_kerbosch_test.go
@@ -53,7 +53,7 @@ func TestDegeneracyOrdering(t *testing.T) {
 		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -93,7 +93,7 @@ func TestKCore(t *testing.T) {
 		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -175,7 +175,7 @@ func TestBronKerbosch(t *testing.T) {
 		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
diff --git a/graph/topo/clique_graph_test.go b/graph/topo/clique_graph_test.go
index 4ae692ca..1f2cd608 100644
--- a/graph/topo/clique_graph_test.go
+++ b/graph/topo/clique_graph_test.go
@@ -92,7 +92,7 @@ func TestCliqueGraph(t *testing.T) {
 		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
diff --git a/graph/topo/johnson_cycles.go b/graph/topo/johnson_cycles.go
index 60390fb7..8122a57e 100644
--- a/graph/topo/johnson_cycles.go
+++ b/graph/topo/johnson_cycles.go
@@ -142,14 +142,15 @@ func johnsonGraphFrom(g graph.Directed) johnsonGraph {
 		succ:  make(map[int64]set.Int64s),
 	}
 	for i, u := range nodes {
-		c.index[u.ID()] = i
-		for _, v := range g.From(u) {
-			if c.succ[u.ID()] == nil {
-				c.succ[u.ID()] = make(set.Int64s)
-				c.nodes.Add(u.ID())
+		uid := u.ID()
+		c.index[uid] = i
+		for _, v := range g.From(uid) {
+			if c.succ[uid] == nil {
+				c.succ[uid] = make(set.Int64s)
+				c.nodes.Add(uid)
 			}
 			c.nodes.Add(v.ID())
-			c.succ[u.ID()].Add(v.ID())
+			c.succ[uid].Add(v.ID())
 		}
 	}
 	return c
@@ -247,31 +248,31 @@ func (g johnsonGraph) Nodes() []graph.Node {
 }
 
 // Successors is required to satisfy Tarjan.
-func (g johnsonGraph) From(n graph.Node) []graph.Node {
-	adj := g.succ[n.ID()]
+func (g johnsonGraph) From(id int64) []graph.Node {
+	adj := g.succ[id]
 	if len(adj) == 0 {
 		return nil
 	}
 	succ := make([]graph.Node, 0, len(adj))
-	for n := range adj {
-		succ = append(succ, johnsonGraphNode(n))
+	for id := range adj {
+		succ = append(succ, johnsonGraphNode(id))
 	}
 	return succ
 }
 
-func (johnsonGraph) Has(graph.Node) bool {
+func (johnsonGraph) Has(int64) bool {
 	panic("topo: unintended use of johnsonGraph")
 }
-func (johnsonGraph) HasEdgeBetween(_, _ graph.Node) bool {
+func (johnsonGraph) HasEdgeBetween(_, _ int64) bool {
 	panic("topo: unintended use of johnsonGraph")
 }
-func (johnsonGraph) Edge(_, _ graph.Node) graph.Edge {
+func (johnsonGraph) Edge(_, _ int64) graph.Edge {
 	panic("topo: unintended use of johnsonGraph")
 }
-func (johnsonGraph) HasEdgeFromTo(_, _ graph.Node) bool {
+func (johnsonGraph) HasEdgeFromTo(_, _ int64) bool {
 	panic("topo: unintended use of johnsonGraph")
 }
-func (johnsonGraph) To(graph.Node) []graph.Node {
+func (johnsonGraph) To(int64) []graph.Node {
 	panic("topo: unintended use of johnsonGraph")
 }
 
diff --git a/graph/topo/johnson_cycles_test.go b/graph/topo/johnson_cycles_test.go
index 31c296fb..2f47d3a1 100644
--- a/graph/topo/johnson_cycles_test.go
+++ b/graph/topo/johnson_cycles_test.go
@@ -88,7 +88,7 @@ func TestDirectedCyclesIn(t *testing.T) {
 		g.AddNode(simple.Node(-10)) // Make sure we test graphs with sparse IDs.
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
diff --git a/graph/topo/paton_cycles.go b/graph/topo/paton_cycles.go
index 3c1c2a8c..5d4d0751 100644
--- a/graph/topo/paton_cycles.go
+++ b/graph/topo/paton_cycles.go
@@ -35,7 +35,7 @@ func UndirectedCyclesIn(g graph.Undirected) [][]graph.Node {
 			u := tree.Pop()
 			uid := u.ID()
 			adj := from[uid]
-			for _, v := range g.From(u) {
+			for _, v := range g.From(uid) {
 				vid := v.ID()
 				switch {
 				case uid == vid:
diff --git a/graph/topo/paton_cycles_test.go b/graph/topo/paton_cycles_test.go
index 2afe2a24..620558ed 100644
--- a/graph/topo/paton_cycles_test.go
+++ b/graph/topo/paton_cycles_test.go
@@ -77,7 +77,7 @@ func TestUndirectedCyclesIn(t *testing.T) {
 		g.AddNode(simple.Node(-10)) // Make sure we test graphs with sparse IDs.
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
diff --git a/graph/topo/tarjan.go b/graph/topo/tarjan.go
index 99f9ec2e..28f50e24 100644
--- a/graph/topo/tarjan.go
+++ b/graph/topo/tarjan.go
@@ -95,15 +95,15 @@ func TarjanSCC(g graph.Directed) [][]graph.Node {
 
 func tarjanSCCstabilized(g graph.Directed, order func([]graph.Node)) [][]graph.Node {
 	nodes := g.Nodes()
-	var succ func(graph.Node) []graph.Node
+	var succ func(id int64) []graph.Node
 	if order == nil {
 		succ = g.From
 	} else {
 		order(nodes)
 		ordered.Reverse(nodes)
 
-		succ = func(n graph.Node) []graph.Node {
-			to := g.From(n)
+		succ = func(id int64) []graph.Node {
+			to := g.From(id)
 			order(to)
 			ordered.Reverse(to)
 			return to
@@ -131,7 +131,7 @@ func tarjanSCCstabilized(g graph.Directed, order func([]graph.Node)) [][]graph.N
 // http://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm?oldid=642744644
 //
 type tarjan struct {
-	succ func(graph.Node) []graph.Node
+	succ func(id int64) []graph.Node
 
 	index      int
 	indexTable map[int64]int
@@ -156,7 +156,7 @@ func (t *tarjan) strongconnect(v graph.Node) {
 	t.onStack.Add(vID)
 
 	// Consider successors of v.
-	for _, w := range t.succ(v) {
+	for _, w := range t.succ(vID) {
 		wID := w.ID()
 		if t.indexTable[wID] == 0 {
 			// Successor w has not yet been visited; recur on it.
diff --git a/graph/topo/tarjan_test.go b/graph/topo/tarjan_test.go
index 9ddb8b25..01a08363 100644
--- a/graph/topo/tarjan_test.go
+++ b/graph/topo/tarjan_test.go
@@ -132,7 +132,7 @@ func TestSort(t *testing.T) {
 		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -163,7 +163,7 @@ func TestTarjanSCC(t *testing.T) {
 		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -290,7 +290,7 @@ func TestSortStabilized(t *testing.T) {
 		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
diff --git a/graph/topo/topo.go b/graph/topo/topo.go
index 335f7b9a..80945cf6 100644
--- a/graph/topo/topo.go
+++ b/graph/topo/topo.go
@@ -18,9 +18,9 @@ func IsPathIn(g graph.Graph, path []graph.Node) bool {
 	case 0:
 		return true
 	case 1:
-		return g.Has(path[0])
+		return g.Has(path[0].ID())
 	default:
-		var canReach func(u, v graph.Node) bool
+		var canReach func(uid, vid int64) bool
 		switch g := g.(type) {
 		case graph.Directed:
 			canReach = g.HasEdgeFromTo
@@ -29,7 +29,7 @@ func IsPathIn(g graph.Graph, path []graph.Node) bool {
 		}
 
 		for i, u := range path[:len(path)-1] {
-			if !canReach(u, path[i+1]) {
+			if !canReach(u.ID(), path[i+1].ID()) {
 				return false
 			}
 		}
diff --git a/graph/topo/topo_test.go b/graph/topo/topo_test.go
index bd43bcff..0f32dad6 100644
--- a/graph/topo/topo_test.go
+++ b/graph/topo/topo_test.go
@@ -71,11 +71,11 @@ func TestPathExistsInUndirected(t *testing.T) {
 		g := simple.NewUndirectedGraph()
 
 		for u, e := range test.g {
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				if !g.Has(simple.Node(v)) {
+				if !g.Has(int64(v)) {
 					g.AddNode(simple.Node(v))
 				}
 				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
@@ -110,11 +110,11 @@ func TestPathExistsInDirected(t *testing.T) {
 		g := simple.NewDirectedGraph()
 
 		for u, e := range test.g {
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				if !g.Has(simple.Node(v)) {
+				if !g.Has(int64(v)) {
 					g.AddNode(simple.Node(v))
 				}
 				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
@@ -147,11 +147,11 @@ func TestConnectedComponents(t *testing.T) {
 		g := simple.NewUndirectedGraph()
 
 		for u, e := range test.g {
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				if !g.Has(simple.Node(v)) {
+				if !g.Has(int64(v)) {
 					g.AddNode(simple.Node(v))
 				}
 				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
diff --git a/graph/traverse/traverse.go b/graph/traverse/traverse.go
index ffdcbb81..b26a10ad 100644
--- a/graph/traverse/traverse.go
+++ b/graph/traverse/traverse.go
@@ -40,17 +40,19 @@ func (b *BreadthFirst) Walk(g graph.Graph, from graph.Node, until func(n graph.N
 		if until != nil && until(t, depth) {
 			return t
 		}
-		for _, n := range g.From(t) {
-			if b.EdgeFilter != nil && !b.EdgeFilter(g.Edge(t, n)) {
+		tid := t.ID()
+		for _, n := range g.From(tid) {
+			nid := n.ID()
+			if b.EdgeFilter != nil && !b.EdgeFilter(g.Edge(tid, nid)) {
 				continue
 			}
-			if b.visited.Has(n.ID()) {
+			if b.visited.Has(nid) {
 				continue
 			}
 			if b.Visit != nil {
 				b.Visit(t, n)
 			}
-			b.visited.Add(n.ID())
+			b.visited.Add(nid)
 			children++
 			b.queue.Enqueue(n)
 		}
@@ -125,17 +127,19 @@ func (d *DepthFirst) Walk(g graph.Graph, from graph.Node, until func(graph.Node)
 		if until != nil && until(t) {
 			return t
 		}
-		for _, n := range g.From(t) {
-			if d.EdgeFilter != nil && !d.EdgeFilter(g.Edge(t, n)) {
+		tid := t.ID()
+		for _, n := range g.From(tid) {
+			nid := n.ID()
+			if d.EdgeFilter != nil && !d.EdgeFilter(g.Edge(tid, nid)) {
 				continue
 			}
-			if d.visited.Has(n.ID()) {
+			if d.visited.Has(nid) {
 				continue
 			}
 			if d.Visit != nil {
 				d.Visit(t, n)
 			}
-			d.visited.Add(n.ID())
+			d.visited.Add(nid)
 			d.stack.Push(n)
 		}
 	}
diff --git a/graph/traverse/traverse_test.go b/graph/traverse/traverse_test.go
index 8a5819a1..cc2cd652 100644
--- a/graph/traverse/traverse_test.go
+++ b/graph/traverse/traverse_test.go
@@ -136,7 +136,7 @@ func TestBreadthFirst(t *testing.T) {
 		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -224,7 +224,7 @@ func TestDepthFirst(t *testing.T) {
 		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
@@ -285,11 +285,11 @@ func TestWalkAll(t *testing.T) {
 		g := simple.NewUndirectedGraph()
 
 		for u, e := range test.g {
-			if !g.Has(simple.Node(u)) {
+			if !g.Has(int64(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				if !g.Has(simple.Node(v)) {
+				if !g.Has(int64(v)) {
 					g.AddNode(simple.Node(v))
 				}
 				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
diff --git a/graph/undirect.go b/graph/undirect.go
index 97d47a06..49ba62bd 100644
--- a/graph/undirect.go
+++ b/graph/undirect.go
@@ -12,20 +12,20 @@ type Undirect struct {
 var _ Undirected = Undirect{}
 
 // Has returns whether the node exists within the graph.
-func (g Undirect) Has(n Node) bool { return g.G.Has(n) }
+func (g Undirect) Has(id int64) bool { return g.G.Has(id) }
 
 // Nodes returns all the nodes in the graph.
 func (g Undirect) Nodes() []Node { return g.G.Nodes() }
 
 // From returns all nodes in g that can be reached directly from u.
-func (g Undirect) From(u Node) []Node {
+func (g Undirect) From(uid int64) []Node {
 	var nodes []Node
 	seen := make(map[int64]struct{})
-	for _, n := range g.G.From(u) {
+	for _, n := range g.G.From(uid) {
 		seen[n.ID()] = struct{}{}
 		nodes = append(nodes, n)
 	}
-	for _, n := range g.G.To(u) {
+	for _, n := range g.G.To(uid) {
 		id := n.ID()
 		if _, ok := seen[id]; ok {
 			continue
@@ -37,21 +37,21 @@ func (g Undirect) From(u Node) []Node {
 }
 
 // HasEdgeBetween returns whether an edge exists between nodes x and y.
-func (g Undirect) HasEdgeBetween(x, y Node) bool { return g.G.HasEdgeBetween(x, y) }
+func (g Undirect) HasEdgeBetween(xid, yid int64) bool { return g.G.HasEdgeBetween(xid, yid) }
 
 // Edge returns the edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
 // If an edge exists, the Edge returned is an EdgePair. The weight of
 // the edge is determined by applying the Merge func to the weights of the
 // edges between u and v.
-func (g Undirect) Edge(u, v Node) Edge { return g.EdgeBetween(u, v) }
+func (g Undirect) Edge(uid, vid int64) Edge { return g.EdgeBetween(uid, vid) }
 
 // EdgeBetween returns the edge between nodes x and y. If an edge exists, the
 // Edge returned is an EdgePair. The weight of the edge is determined by
 // applying the Merge func to the weights of edges between x and y.
-func (g Undirect) EdgeBetween(x, y Node) Edge {
-	fe := g.G.Edge(x, y)
-	re := g.G.Edge(y, x)
+func (g Undirect) EdgeBetween(xid, yid int64) Edge {
+	fe := g.G.Edge(xid, yid)
+	re := g.G.Edge(yid, xid)
 	if fe == nil && re == nil {
 		return nil
 	}
@@ -91,20 +91,20 @@ var (
 )
 
 // Has returns whether the node exists within the graph.
-func (g UndirectWeighted) Has(n Node) bool { return g.G.Has(n) }
+func (g UndirectWeighted) Has(id int64) bool { return g.G.Has(id) }
 
 // Nodes returns all the nodes in the graph.
 func (g UndirectWeighted) Nodes() []Node { return g.G.Nodes() }
 
 // From returns all nodes in g that can be reached directly from u.
-func (g UndirectWeighted) From(u Node) []Node {
+func (g UndirectWeighted) From(uid int64) []Node {
 	var nodes []Node
 	seen := make(map[int64]struct{})
-	for _, n := range g.G.From(u) {
+	for _, n := range g.G.From(uid) {
 		seen[n.ID()] = struct{}{}
 		nodes = append(nodes, n)
 	}
-	for _, n := range g.G.To(u) {
+	for _, n := range g.G.To(uid) {
 		id := n.ID()
 		if _, ok := seen[id]; ok {
 			continue
@@ -116,44 +116,46 @@ func (g UndirectWeighted) From(u Node) []Node {
 }
 
 // HasEdgeBetween returns whether an edge exists between nodes x and y.
-func (g UndirectWeighted) HasEdgeBetween(x, y Node) bool { return g.G.HasEdgeBetween(x, y) }
+func (g UndirectWeighted) HasEdgeBetween(xid, yid int64) bool { return g.G.HasEdgeBetween(xid, yid) }
 
 // Edge returns the edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
 // If an edge exists, the Edge returned is an EdgePair. The weight of
 // the edge is determined by applying the Merge func to the weights of the
 // edges between u and v.
-func (g UndirectWeighted) Edge(u, v Node) Edge { return g.WeightedEdgeBetween(u, v) }
+func (g UndirectWeighted) Edge(uid, vid int64) Edge { return g.WeightedEdgeBetween(uid, vid) }
 
 // WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
 // The node v must be directly reachable from u as defined by the From method.
 // If an edge exists, the Edge returned is an EdgePair. The weight of
 // the edge is determined by applying the Merge func to the weights of the
 // edges between u and v.
-func (g UndirectWeighted) WeightedEdge(u, v Node) WeightedEdge { return g.WeightedEdgeBetween(u, v) }
+func (g UndirectWeighted) WeightedEdge(uid, vid int64) WeightedEdge {
+	return g.WeightedEdgeBetween(uid, vid)
+}
 
 // EdgeBetween returns the edge between nodes x and y. If an edge exists, the
 // Edge returned is an EdgePair. The weight of the edge is determined by
 // applying the Merge func to the weights of edges between x and y.
-func (g UndirectWeighted) EdgeBetween(x, y Node) Edge {
-	return g.WeightedEdgeBetween(x, y)
+func (g UndirectWeighted) EdgeBetween(xid, yid int64) Edge {
+	return g.WeightedEdgeBetween(xid, yid)
 }
 
 // WeightedEdgeBetween returns the weighted edge between nodes x and y. If an edge exists, the
 // Edge returned is an EdgePair. The weight of the edge is determined by
 // applying the Merge func to the weights of edges between x and y.
-func (g UndirectWeighted) WeightedEdgeBetween(x, y Node) WeightedEdge {
-	fe := g.G.Edge(x, y)
-	re := g.G.Edge(y, x)
+func (g UndirectWeighted) WeightedEdgeBetween(xid, yid int64) WeightedEdge {
+	fe := g.G.Edge(xid, yid)
+	re := g.G.Edge(yid, xid)
 	if fe == nil && re == nil {
 		return nil
 	}
 
-	f, ok := g.G.Weight(x, y)
+	f, ok := g.G.Weight(xid, yid)
 	if !ok {
 		f = g.Absent
 	}
-	r, ok := g.G.Weight(y, x)
+	r, ok := g.G.Weight(yid, xid)
 	if !ok {
 		r = g.Absent
 	}
@@ -171,15 +173,15 @@ func (g UndirectWeighted) WeightedEdgeBetween(x, y Node) WeightedEdge {
 // If x and y are the same node the internal node weight is returned. If there is no joining
 // edge between the two nodes the weight value returned is zero. Weight returns true if an edge
 // exists between x and y or if x and y have the same ID, false otherwise.
-func (g UndirectWeighted) Weight(x, y Node) (w float64, ok bool) {
-	fe := g.G.Edge(x, y)
-	re := g.G.Edge(y, x)
+func (g UndirectWeighted) Weight(xid, yid int64) (w float64, ok bool) {
+	fe := g.G.Edge(xid, yid)
+	re := g.G.Edge(yid, xid)
 
-	f, fOk := g.G.Weight(x, y)
+	f, fOk := g.G.Weight(xid, yid)
 	if !fOk {
 		f = g.Absent
 	}
-	r, rOK := g.G.Weight(y, x)
+	r, rOK := g.G.Weight(yid, xid)
 	if !rOK {
 		r = g.Absent
 	}
diff --git a/graph/undirect_test.go b/graph/undirect_test.go
index 462de2e7..5304e834 100644
--- a/graph/undirect_test.go
+++ b/graph/undirect_test.go
@@ -123,8 +123,8 @@ func TestUndirect(t *testing.T) {
 		src := graph.Undirect{G: g}
 		dst := simple.NewUndirectedMatrixFrom(src.Nodes(), 0, 0, 0)
 		for _, u := range src.Nodes() {
-			for _, v := range src.From(u) {
-				dst.SetEdge(src.Edge(u, v))
+			for _, v := range src.From(u.ID()) {
+				dst.SetEdge(src.Edge(u.ID(), v.ID()))
 			}
 		}
 
@@ -148,8 +148,8 @@ func TestUndirectWeighted(t *testing.T) {
 		src := graph.UndirectWeighted{G: g, Absent: test.absent, Merge: test.merge}
 		dst := simple.NewUndirectedMatrixFrom(src.Nodes(), 0, 0, 0)
 		for _, u := range src.Nodes() {
-			for _, v := range src.From(u) {
-				dst.SetWeightedEdge(src.WeightedEdge(u, v))
+			for _, v := range src.From(u.ID()) {
+				dst.SetWeightedEdge(src.WeightedEdge(u.ID(), v.ID()))
 			}
 		}