diff --git a/graph/community/bisect_test.go b/graph/community/bisect_test.go
index 4c2498ee..ab03814a 100644
--- a/graph/community/bisect_test.go
+++ b/graph/community/bisect_test.go
@@ -10,8 +10,8 @@ import (
 	"sort"
 	"testing"
 
+	"gonum.org/v1/gonum/graph"
 	"gonum.org/v1/gonum/graph/internal/ordered"
-
 	"gonum.org/v1/gonum/graph/simple"
 )
 
@@ -24,10 +24,10 @@ func ExampleProfile_simple() {
 	//  |/     \|
 	//  1       5
 	//
-	g := simple.NewUndirectedGraph(0, 0)
+	g := simple.NewUndirectedGraph()
 	for u, e := range smallDumbell {
 		for v := range e {
-			g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
 		}
 	}
 
@@ -56,27 +56,27 @@ func ExampleProfile_simple() {
 	// Low:3.5 High:10 Score:0 Communities:[[0] [1] [2] [3] [4] [5]] Q=-0.607
 }
 
-var friends, enemies *simple.UndirectedGraph
+var friends, enemies *simple.WeightedUndirectedGraph
 
 func init() {
-	friends = simple.NewUndirectedGraph(0, 0)
+	friends = simple.NewWeightedUndirectedGraph(0, 0)
 	for u, e := range middleEast.friends {
 		// Ensure unconnected nodes are included.
 		if !friends.Has(simple.Node(u)) {
 			friends.AddNode(simple.Node(u))
 		}
 		for v := range e {
-			friends.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			friends.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
 		}
 	}
-	enemies = simple.NewUndirectedGraph(0, 0)
+	enemies = simple.NewWeightedUndirectedGraph(0, 0)
 	for u, e := range middleEast.enemies {
 		// Ensure unconnected nodes are included.
 		if !enemies.Has(simple.Node(u)) {
 			enemies.AddNode(simple.Node(u))
 		}
 		for v := range e {
-			enemies.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: -1})
+			enemies.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: -1})
 		}
 	}
 }
@@ -112,8 +112,8 @@ func ExampleProfile_multiplex() {
 	// Output:
 	// Low:0.1 High:0.72 Score:26 Communities:[[0] [1 7 9 12] [2 8 11] [3 4 5 10] [6]] Q=[24.7 1.97]
 	// Low:0.72 High:1.1 Score:24 Communities:[[0 6] [1 7 9 12] [2 8 11] [3 4 5 10]] Q=[16.9 14.1]
-	// Low:1.1 High:1.2 Score:18 Communities:[[0 2 6 11] [1 7 9 12] [3 4 5 8 10]] Q=[9.16 25.1]
-	// Low:1.2 High:1.6 Score:10 Communities:[[0 3 4 5 6 10] [1 7 9 12] [2 8 11]] Q=[11.4 24.1]
+	// Low:1.1 High:1.1 Score:18 Communities:[[0 2 6 11] [1 7 9 12] [3 4 5 8 10]] Q=[9.16 25.1]
+	// Low:1.1 High:1.6 Score:10 Communities:[[0 3 4 5 6 10] [1 7 9 12] [2 8 11]] Q=[11.5 23.9]
 	// Low:1.6 High:1.6 Score:8 Communities:[[0 1 6 7 9 12] [2 8 11] [3 4 5 10]] Q=[5.56 39.8]
 	// Low:1.6 High:1.8 Score:2 Communities:[[0 2 3 4 5 6 10] [1 7 8 9 11 12]] Q=[-1.82 48.6]
 	// Low:1.8 High:2.3 Score:-6 Communities:[[0 2 3 4 5 6 8 10 11] [1 7 9 12]] Q=[-5 57.5]
@@ -124,77 +124,119 @@ func ExampleProfile_multiplex() {
 
 func TestProfileUndirected(t *testing.T) {
 	for _, test := range communityUndirectedQTests {
-		g := simple.NewUndirectedGraph(0, 0)
+		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
 			}
 		}
 
-		fn := ModularScore(g, Weight, 10, nil)
-		p, err := Profile(fn, true, 1e-3, 0.1, 10)
-		if err != nil {
-			t.Errorf("%s: unexpected error: %v", test.name, err)
+		testProfileUndirected(t, test, g)
+	}
+}
+
+func TestProfileWeightedUndirected(t *testing.T) {
+	for _, test := range communityUndirectedQTests {
+		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)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
 		}
 
-		const tries = 1000
-		for i, d := range p {
-			var score float64
-			for i := 0; i < tries; i++ {
-				score, _ = fn(d.Low)
-				if score >= d.Score {
-					break
-				}
-			}
-			if score < d.Score {
-				t.Errorf("%s: failed to recover low end score: got: %v want: %v", test.name, score, d.Score)
-			}
-			if i != 0 && d.Score >= p[i-1].Score {
-				t.Errorf("%s: not monotonically decreasing: %v -> %v", test.name, p[i-1], d)
+		testProfileUndirected(t, test, g)
+	}
+}
+
+func testProfileUndirected(t *testing.T, test communityUndirectedQTest, g graph.Undirected) {
+	fn := ModularScore(g, Weight, 10, nil)
+	p, err := Profile(fn, true, 1e-3, 0.1, 10)
+	if err != nil {
+		t.Errorf("%s: unexpected error: %v", test.name, err)
+	}
+
+	const tries = 1000
+	for i, d := range p {
+		var score float64
+		for i := 0; i < tries; i++ {
+			score, _ = fn(d.Low)
+			if score >= d.Score {
+				break
 			}
 		}
+		if score < d.Score {
+			t.Errorf("%s: failed to recover low end score: got: %v want: %v", test.name, score, d.Score)
+		}
+		if i != 0 && d.Score >= p[i-1].Score {
+			t.Errorf("%s: not monotonically decreasing: %v -> %v", test.name, p[i-1], d)
+		}
 	}
 }
 
 func TestProfileDirected(t *testing.T) {
 	for _, test := range communityDirectedQTests {
-		g := simple.NewDirectedGraph(0, 0)
+		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
 			}
 		}
 
-		fn := ModularScore(g, Weight, 10, nil)
-		p, err := Profile(fn, true, 1e-3, 0.1, 10)
-		if err != nil {
-			t.Errorf("%s: unexpected error: %v", test.name, err)
+		testProfileDirected(t, test, g)
+	}
+}
+
+func TestProfileWeightedDirected(t *testing.T) {
+	for _, test := range communityDirectedQTests {
+		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)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
 		}
 
-		const tries = 1000
-		for i, d := range p {
-			var score float64
-			for i := 0; i < tries; i++ {
-				score, _ = fn(d.Low)
-				if score >= d.Score {
-					break
-				}
-			}
-			if score < d.Score {
-				t.Errorf("%s: failed to recover low end score: got: %v want: %v", test.name, score, d.Score)
-			}
-			if i != 0 && d.Score >= p[i-1].Score {
-				t.Errorf("%s: not monotonically decreasing: %v -> %v", test.name, p[i-1], d)
+		testProfileDirected(t, test, g)
+	}
+}
+
+func testProfileDirected(t *testing.T, test communityDirectedQTest, g graph.Directed) {
+	fn := ModularScore(g, Weight, 10, nil)
+	p, err := Profile(fn, true, 1e-3, 0.1, 10)
+	if err != nil {
+		t.Errorf("%s: unexpected error: %v", test.name, err)
+	}
+
+	const tries = 1000
+	for i, d := range p {
+		var score float64
+		for i := 0; i < tries; i++ {
+			score, _ = fn(d.Low)
+			if score >= d.Score {
+				break
 			}
 		}
+		if score < d.Score {
+			t.Errorf("%s: failed to recover low end score: got: %v want: %v", test.name, score, d.Score)
+		}
+		if i != 0 && d.Score >= p[i-1].Score {
+			t.Errorf("%s: not monotonically decreasing: %v -> %v", test.name, p[i-1], d)
+		}
 	}
 }
 
diff --git a/graph/community/louvain_common.go b/graph/community/louvain_common.go
index 3258f125..987776c0 100644
--- a/graph/community/louvain_common.go
+++ b/graph/community/louvain_common.go
@@ -356,7 +356,8 @@ const (
 )
 
 // positiveWeightFuncFor returns a constructed weight function for the
-// positively weighted g.
+// positively weighted g. Unweighted graphs have unit weight for existing
+// edges.
 func positiveWeightFuncFor(g graph.Graph) func(x, y graph.Node) float64 {
 	if wg, ok := g.(graph.Weighted); ok {
 		return func(x, y graph.Node) float64 {
@@ -375,16 +376,13 @@ func positiveWeightFuncFor(g graph.Graph) func(x, y graph.Node) float64 {
 		if e == nil {
 			return 0
 		}
-		w := e.Weight()
-		if w < 0 {
-			panic(negativeWeight)
-		}
-		return w
+		return 1
 	}
 }
 
 // negativeWeightFuncFor returns a constructed weight function for the
-// negatively weighted g.
+// negatively weighted g. Unweighted graphs have unit weight for existing
+// edges.
 func negativeWeightFuncFor(g graph.Graph) func(x, y graph.Node) float64 {
 	if wg, ok := g.(graph.Weighted); ok {
 		return func(x, y graph.Node) float64 {
@@ -403,11 +401,7 @@ func negativeWeightFuncFor(g graph.Graph) func(x, y graph.Node) float64 {
 		if e == nil {
 			return 0
 		}
-		w := e.Weight()
-		if w > 0 {
-			panic(positiveWeight)
-		}
-		return -w
+		return 1
 	}
 }
 
diff --git a/graph/community/louvain_directed_multiplex_test.go b/graph/community/louvain_directed_multiplex_test.go
index 6d0bf530..f3870a64 100644
--- a/graph/community/louvain_directed_multiplex_test.go
+++ b/graph/community/louvain_directed_multiplex_test.go
@@ -647,12 +647,32 @@ func TestLouvainDirectedMultiplex(t *testing.T) {
 }
 
 func TestNonContiguousDirectedMultiplex(t *testing.T) {
-	g := simple.NewDirectedGraph(0, 0)
+	g := simple.NewDirectedGraph()
+	for _, e := range []simple.Edge{
+		{F: simple.Node(0), T: simple.Node(1)},
+		{F: simple.Node(4), T: simple.Node(5)},
+	} {
+		g.SetEdge(e)
+	}
+
+	func() {
+		defer func() {
+			r := recover()
+			if r != nil {
+				t.Error("unexpected panic with non-contiguous ID range")
+			}
+		}()
+		ModularizeMultiplex(DirectedLayers{g}, nil, nil, true, nil)
+	}()
+}
+
+func TestNonContiguousWeightedDirectedMultiplex(t *testing.T) {
+	g := simple.NewWeightedDirectedGraph(0, 0)
 	for _, e := range []simple.Edge{
 		{F: simple.Node(0), T: simple.Node(1), W: 1},
 		{F: simple.Node(4), T: simple.Node(5), W: 1},
 	} {
-		g.SetEdge(e)
+		g.SetWeightedEdge(e)
 	}
 
 	func() {
@@ -677,7 +697,7 @@ func directedMultiplexFrom(raw []layer) (DirectedLayers, []float64, error) {
 	var layers []graph.Directed
 	var weights []float64
 	for _, l := range raw {
-		g := simple.NewDirectedGraph(0, 0)
+		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)) {
@@ -688,7 +708,7 @@ func directedMultiplexFrom(raw []layer) (DirectedLayers, []float64, error) {
 				if l.edgeWeight != 0 {
 					w = l.edgeWeight
 				}
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: w})
+				g.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: w})
 			}
 		}
 		layers = append(layers, g)
diff --git a/graph/community/louvain_directed_test.go b/graph/community/louvain_directed_test.go
index 25373e80..6fc5487d 100644
--- a/graph/community/louvain_directed_test.go
+++ b/graph/community/louvain_directed_test.go
@@ -17,13 +17,15 @@ import (
 	"gonum.org/v1/gonum/graph/simple"
 )
 
-var communityDirectedQTests = []struct {
+type communityDirectedQTest struct {
 	name       string
 	g          []intset
 	structures []structure
 
 	wantLevels []level
-}{
+}
+
+var communityDirectedQTests = []communityDirectedQTest{
 	{
 		name: "simple_directed",
 		g:    simpleDirected,
@@ -199,194 +201,258 @@ var communityDirectedQTests = []struct {
 
 func TestCommunityQDirected(t *testing.T) {
 	for _, test := range communityDirectedQTests {
-		g := simple.NewDirectedGraph(0, 0)
+		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
 			}
 		}
-		for _, structure := range test.structures {
-			communities := make([][]graph.Node, len(structure.memberships))
-			for i, c := range structure.memberships {
-				for n := range c {
-					communities[i] = append(communities[i], simple.Node(n))
-				}
+
+		testCommunityQDirected(t, test, g)
+	}
+}
+
+func TestCommunityQWeightedDirected(t *testing.T) {
+	for _, test := range communityDirectedQTests {
+		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)) {
+				g.AddNode(simple.Node(u))
 			}
-			got := Q(g, communities, structure.resolution)
-			if !floats.EqualWithinAbsOrRel(got, structure.want, structure.tol, structure.tol) && !math.IsNaN(structure.want) {
-				for _, c := range communities {
-					sort.Sort(ordered.ByID(c))
-				}
-				t.Errorf("unexpected Q value for %q %v: got: %v want: %v",
-					test.name, communities, got, structure.want)
+			for v := range e {
+				g.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
 			}
 		}
+
+		testCommunityQDirected(t, test, g)
+	}
+}
+
+func testCommunityQDirected(t *testing.T, test communityDirectedQTest, g graph.Directed) {
+	for _, structure := range test.structures {
+		communities := make([][]graph.Node, len(structure.memberships))
+		for i, c := range structure.memberships {
+			for n := range c {
+				communities[i] = append(communities[i], simple.Node(n))
+			}
+		}
+		got := Q(g, communities, structure.resolution)
+		if !floats.EqualWithinAbsOrRel(got, structure.want, structure.tol, structure.tol) && !math.IsNaN(structure.want) {
+			for _, c := range communities {
+				sort.Sort(ordered.ByID(c))
+			}
+			t.Errorf("unexpected Q value for %q %v: got: %v want: %v",
+				test.name, communities, got, structure.want)
+		}
 	}
 }
 
 func TestCommunityDeltaQDirected(t *testing.T) {
-tests:
 	for _, test := range communityDirectedQTests {
-		g := simple.NewDirectedGraph(0, 0)
+		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
 			}
 		}
 
-		rnd := rand.New(rand.NewSource(1)).Intn
-		for _, structure := range test.structures {
-			communityOf := make(map[int64]int)
-			communities := make([][]graph.Node, len(structure.memberships))
+		testCommunityDeltaQDirected(t, test, g)
+	}
+}
+
+func TestCommunityDeltaQWeightedDirected(t *testing.T) {
+	for _, test := range communityDirectedQTests {
+		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)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
+
+		testCommunityDeltaQDirected(t, test, g)
+	}
+}
+
+func testCommunityDeltaQDirected(t *testing.T, test communityDirectedQTest, g graph.Directed) {
+	rnd := rand.New(rand.NewSource(1)).Intn
+	for _, structure := range test.structures {
+		communityOf := make(map[int64]int)
+		communities := make([][]graph.Node, len(structure.memberships))
+		for i, c := range structure.memberships {
+			for n := range c {
+				n := int64(n)
+				communityOf[n] = i
+				communities[i] = append(communities[i], simple.Node(n))
+			}
+			sort.Sort(ordered.ByID(communities[i]))
+		}
+
+		before := Q(g, communities, structure.resolution)
+
+		l := newDirectedLocalMover(reduceDirected(g, nil), communities, structure.resolution)
+		if l == nil {
+			if !math.IsNaN(before) {
+				t.Errorf("unexpected nil localMover with non-NaN Q graph: Q=%.4v", before)
+			}
+			return
+		}
+
+		// This is done to avoid run-to-run
+		// variation due to map iteration order.
+		sort.Sort(ordered.ByID(l.nodes))
+
+		l.shuffle(rnd)
+
+		for _, target := range l.nodes {
+			got, gotDst, gotSrc := l.deltaQ(target)
+
+			want, wantDst := math.Inf(-1), -1
+			migrated := make([][]graph.Node, len(structure.memberships))
 			for i, c := range structure.memberships {
 				for n := range c {
 					n := int64(n)
-					communityOf[n] = i
-					communities[i] = append(communities[i], simple.Node(n))
-				}
-				sort.Sort(ordered.ByID(communities[i]))
-			}
-
-			before := Q(g, communities, structure.resolution)
-
-			l := newDirectedLocalMover(reduceDirected(g, nil), communities, structure.resolution)
-			if l == nil {
-				if !math.IsNaN(before) {
-					t.Errorf("unexpected nil localMover with non-NaN Q graph: Q=%.4v", before)
-				}
-				continue tests
-			}
-
-			// This is done to avoid run-to-run
-			// variation due to map iteration order.
-			sort.Sort(ordered.ByID(l.nodes))
-
-			l.shuffle(rnd)
-
-			for _, target := range l.nodes {
-				got, gotDst, gotSrc := l.deltaQ(target)
-
-				want, wantDst := math.Inf(-1), -1
-				migrated := make([][]graph.Node, len(structure.memberships))
-				for i, c := range structure.memberships {
-					for n := range c {
-						n := int64(n)
-						if n == target.ID() {
-							continue
-						}
-						migrated[i] = append(migrated[i], simple.Node(n))
-					}
-					sort.Sort(ordered.ByID(migrated[i]))
-				}
-
-				for i, c := range structure.memberships {
-					if i == communityOf[target.ID()] {
+					if n == target.ID() {
 						continue
 					}
-					connected := false
-					for n := range c {
-						if g.HasEdgeBetween(simple.Node(n), target) {
-							connected = true
-							break
-						}
-					}
-					if !connected {
-						continue
-					}
-					migrated[i] = append(migrated[i], target)
-					after := Q(g, migrated, structure.resolution)
-					migrated[i] = migrated[i][:len(migrated[i])-1]
-					if after-before > want {
-						want = after - before
-						wantDst = i
-					}
+					migrated[i] = append(migrated[i], simple.Node(n))
 				}
+				sort.Sort(ordered.ByID(migrated[i]))
+			}
 
-				if !floats.EqualWithinAbsOrRel(got, want, structure.tol, structure.tol) || gotDst != wantDst {
-					t.Errorf("unexpected result moving n=%d in c=%d of %s/%.4v: got: %.4v,%d want: %.4v,%d"+
-						"\n\t%v\n\t%v",
-						target.ID(), communityOf[target.ID()], test.name, structure.resolution, got, gotDst, want, wantDst,
-						communities, migrated)
+			for i, c := range structure.memberships {
+				if i == communityOf[target.ID()] {
+					continue
 				}
-				if gotSrc.community != communityOf[target.ID()] {
-					t.Errorf("unexpected source community index: got: %d want: %d", gotSrc, communityOf[target.ID()])
-				} else if communities[gotSrc.community][gotSrc.node].ID() != target.ID() {
-					wantNodeIdx := -1
-					for i, n := range communities[gotSrc.community] {
-						if n.ID() == target.ID() {
-							wantNodeIdx = i
-							break
-						}
+				connected := false
+				for n := range c {
+					if g.HasEdgeBetween(simple.Node(n), target) {
+						connected = true
+						break
 					}
-					t.Errorf("unexpected source node index: got: %d want: %d", gotSrc.node, wantNodeIdx)
 				}
+				if !connected {
+					continue
+				}
+				migrated[i] = append(migrated[i], target)
+				after := Q(g, migrated, structure.resolution)
+				migrated[i] = migrated[i][:len(migrated[i])-1]
+				if after-before > want {
+					want = after - before
+					wantDst = i
+				}
+			}
+
+			if !floats.EqualWithinAbsOrRel(got, want, structure.tol, structure.tol) || gotDst != wantDst {
+				t.Errorf("unexpected result moving n=%d in c=%d of %s/%.4v: got: %.4v,%d want: %.4v,%d"+
+					"\n\t%v\n\t%v",
+					target.ID(), communityOf[target.ID()], test.name, structure.resolution, got, gotDst, want, wantDst,
+					communities, migrated)
+			}
+			if gotSrc.community != communityOf[target.ID()] {
+				t.Errorf("unexpected source community index: got: %d want: %d", gotSrc, communityOf[target.ID()])
+			} else if communities[gotSrc.community][gotSrc.node].ID() != target.ID() {
+				wantNodeIdx := -1
+				for i, n := range communities[gotSrc.community] {
+					if n.ID() == target.ID() {
+						wantNodeIdx = i
+						break
+					}
+				}
+				t.Errorf("unexpected source node index: got: %d want: %d", gotSrc.node, wantNodeIdx)
 			}
 		}
 	}
 }
 
 func TestReduceQConsistencyDirected(t *testing.T) {
-tests:
 	for _, test := range communityDirectedQTests {
-		g := simple.NewDirectedGraph(0, 0)
+		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
 			}
 		}
 
-		for _, structure := range test.structures {
-			if math.IsNaN(structure.want) {
-				continue tests
-			}
+		testReduceQConsistencyDirected(t, test, g)
+	}
+}
 
-			communities := make([][]graph.Node, len(structure.memberships))
-			for i, c := range structure.memberships {
-				for n := range c {
-					communities[i] = append(communities[i], simple.Node(n))
-				}
-				sort.Sort(ordered.ByID(communities[i]))
+func TestReduceQConsistencyWeightedDirected(t *testing.T) {
+	for _, test := range communityDirectedQTests {
+		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)) {
+				g.AddNode(simple.Node(u))
 			}
+			for v := range e {
+				g.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
 
-			gQ := Q(g, communities, structure.resolution)
-			gQnull := Q(g, nil, 1)
+		testReduceQConsistencyDirected(t, test, g)
+	}
+}
 
-			cg0 := reduceDirected(g, nil)
-			cg0Qnull := Q(cg0, cg0.Structure(), 1)
-			if !floats.EqualWithinAbsOrRel(gQnull, cg0Qnull, structure.tol, structure.tol) {
-				t.Errorf("disagreement between null Q from method: %v and function: %v", cg0Qnull, gQnull)
-			}
-			cg0Q := Q(cg0, communities, structure.resolution)
-			if !floats.EqualWithinAbsOrRel(gQ, cg0Q, structure.tol, structure.tol) {
-				t.Errorf("unexpected Q result after initial reduction: got: %v want :%v", cg0Q, gQ)
-			}
+func testReduceQConsistencyDirected(t *testing.T, test communityDirectedQTest, g graph.Directed) {
+	for _, structure := range test.structures {
+		if math.IsNaN(structure.want) {
+			return
+		}
 
-			cg1 := reduceDirected(cg0, communities)
-			cg1Q := Q(cg1, cg1.Structure(), structure.resolution)
-			if !floats.EqualWithinAbsOrRel(gQ, cg1Q, structure.tol, structure.tol) {
-				t.Errorf("unexpected Q result after second reduction: got: %v want :%v", cg1Q, gQ)
+		communities := make([][]graph.Node, len(structure.memberships))
+		for i, c := range structure.memberships {
+			for n := range c {
+				communities[i] = append(communities[i], simple.Node(n))
 			}
+			sort.Sort(ordered.ByID(communities[i]))
+		}
+
+		gQ := Q(g, communities, structure.resolution)
+		gQnull := Q(g, nil, 1)
+
+		cg0 := reduceDirected(g, nil)
+		cg0Qnull := Q(cg0, cg0.Structure(), 1)
+		if !floats.EqualWithinAbsOrRel(gQnull, cg0Qnull, structure.tol, structure.tol) {
+			t.Errorf("disagreement between null Q from method: %v and function: %v", cg0Qnull, gQnull)
+		}
+		cg0Q := Q(cg0, communities, structure.resolution)
+		if !floats.EqualWithinAbsOrRel(gQ, cg0Q, structure.tol, structure.tol) {
+			t.Errorf("unexpected Q result after initial reduction: got: %v want :%v", cg0Q, gQ)
+		}
+
+		cg1 := reduceDirected(cg0, communities)
+		cg1Q := Q(cg1, cg1.Structure(), structure.resolution)
+		if !floats.EqualWithinAbsOrRel(gQ, cg1Q, structure.tol, structure.tol) {
+			t.Errorf("unexpected Q result after second reduction: got: %v want :%v", cg1Q, gQ)
 		}
 	}
 }
 
-var localDirectedMoveTests = []struct {
+type localDirectedMoveTest struct {
 	name       string
 	g          []intset
 	structures []moveStructures
-}{
+}
+
+var localDirectedMoveTests = []localDirectedMoveTest{
 	{
 		name: "blondel",
 		g:    blondel,
@@ -431,39 +497,60 @@ var localDirectedMoveTests = []struct {
 
 func TestMoveLocalDirected(t *testing.T) {
 	for _, test := range localDirectedMoveTests {
-		g := simple.NewDirectedGraph(0, 0)
+		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
 			}
 		}
 
-		for _, structure := range test.structures {
-			communities := make([][]graph.Node, len(structure.memberships))
-			for i, c := range structure.memberships {
-				for n := range c {
-					communities[i] = append(communities[i], simple.Node(n))
-				}
-				sort.Sort(ordered.ByID(communities[i]))
+		testMoveLocalDirected(t, test, g)
+	}
+}
+
+func TestMoveLocalWeightedDirected(t *testing.T) {
+	for _, test := range localDirectedMoveTests {
+		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)) {
+				g.AddNode(simple.Node(u))
 			}
+			for v := range e {
+				g.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
 
-			r := reduceDirected(reduceDirected(g, nil), communities)
+		testMoveLocalDirected(t, test, g)
+	}
+}
 
-			l := newDirectedLocalMover(r, r.communities, structure.resolution)
-			for _, n := range structure.targetNodes {
-				dQ, dst, src := l.deltaQ(n)
-				if dQ > 0 {
-					before := Q(r, l.communities, structure.resolution)
-					l.move(dst, src)
-					after := Q(r, l.communities, structure.resolution)
-					want := after - before
-					if !floats.EqualWithinAbsOrRel(dQ, want, structure.tol, structure.tol) {
-						t.Errorf("unexpected deltaQ: got: %v want: %v", dQ, want)
-					}
+func testMoveLocalDirected(t *testing.T, test localDirectedMoveTest, g graph.Directed) {
+	for _, structure := range test.structures {
+		communities := make([][]graph.Node, len(structure.memberships))
+		for i, c := range structure.memberships {
+			for n := range c {
+				communities[i] = append(communities[i], simple.Node(n))
+			}
+			sort.Sort(ordered.ByID(communities[i]))
+		}
+
+		r := reduceDirected(reduceDirected(g, nil), communities)
+
+		l := newDirectedLocalMover(r, r.communities, structure.resolution)
+		for _, n := range structure.targetNodes {
+			dQ, dst, src := l.deltaQ(n)
+			if dQ > 0 {
+				before := Q(r, l.communities, structure.resolution)
+				l.move(dst, src)
+				after := Q(r, l.communities, structure.resolution)
+				want := after - before
+				if !floats.EqualWithinAbsOrRel(dQ, want, structure.tol, structure.tol) {
+					t.Errorf("unexpected deltaQ: got: %v want: %v", dQ, want)
 				}
 			}
 		}
@@ -471,105 +558,146 @@ func TestMoveLocalDirected(t *testing.T) {
 }
 
 func TestModularizeDirected(t *testing.T) {
-	const louvainIterations = 20
-
 	for _, test := range communityDirectedQTests {
-		g := simple.NewDirectedGraph(0, 0)
+		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
 			}
 		}
 
-		if test.structures[0].resolution != 1 {
-			panic("bad test: expect resolution=1")
-		}
-		want := make([][]graph.Node, len(test.structures[0].memberships))
-		for i, c := range test.structures[0].memberships {
-			for n := range c {
-				want[i] = append(want[i], simple.Node(n))
+		testModularizeDirected(t, test, g)
+	}
+}
+
+func TestModularizeWeightedDirected(t *testing.T) {
+	for _, test := range communityDirectedQTests {
+		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)) {
+				g.AddNode(simple.Node(u))
 			}
-			sort.Sort(ordered.ByID(want[i]))
-		}
-		sort.Sort(ordered.BySliceIDs(want))
-
-		var (
-			got   *ReducedDirected
-			bestQ = math.Inf(-1)
-		)
-		// Modularize is randomised so we do this to
-		// ensure the level tests are consistent.
-		src := rand.New(rand.NewSource(1))
-		for i := 0; i < louvainIterations; i++ {
-			r := Modularize(g, 1, src).(*ReducedDirected)
-			if q := Q(r, nil, 1); q > bestQ || math.IsNaN(q) {
-				bestQ = q
-				got = r
-
-				if math.IsNaN(q) {
-					// Don't try again for non-connected case.
-					break
-				}
-			}
-
-			var qs []float64
-			for p := r; p != nil; p = p.Expanded().(*ReducedDirected) {
-				qs = append(qs, Q(p, nil, 1))
-			}
-
-			// Recovery of Q values is reversed.
-			if reverse(qs); !sort.Float64sAreSorted(qs) {
-				t.Errorf("Q values not monotonically increasing: %.5v", qs)
+			for v := range e {
+				g.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
 			}
 		}
 
-		gotCommunities := got.Communities()
-		for _, c := range gotCommunities {
-			sort.Sort(ordered.ByID(c))
-		}
-		sort.Sort(ordered.BySliceIDs(gotCommunities))
-		if !reflect.DeepEqual(gotCommunities, want) {
-			t.Errorf("unexpected community membership for %s Q=%.4v:\n\tgot: %v\n\twant:%v",
-				test.name, bestQ, gotCommunities, want)
-			continue
-		}
+		testModularizeDirected(t, test, g)
+	}
+}
+
+func testModularizeDirected(t *testing.T, test communityDirectedQTest, g graph.Directed) {
+	const louvainIterations = 20
+
+	if test.structures[0].resolution != 1 {
+		panic("bad test: expect resolution=1")
+	}
+	want := make([][]graph.Node, len(test.structures[0].memberships))
+	for i, c := range test.structures[0].memberships {
+		for n := range c {
+			want[i] = append(want[i], simple.Node(n))
+		}
+		sort.Sort(ordered.ByID(want[i]))
+	}
+	sort.Sort(ordered.BySliceIDs(want))
+
+	var (
+		got   *ReducedDirected
+		bestQ = math.Inf(-1)
+	)
+	// Modularize is randomised so we do this to
+	// ensure the level tests are consistent.
+	src := rand.New(rand.NewSource(1))
+	for i := 0; i < louvainIterations; i++ {
+		r := Modularize(g, 1, src).(*ReducedDirected)
+		if q := Q(r, nil, 1); q > bestQ || math.IsNaN(q) {
+			bestQ = q
+			got = r
 
-		var levels []level
-		for p := got; p != nil; p = p.Expanded().(*ReducedDirected) {
-			var communities [][]graph.Node
-			if p.parent != nil {
-				communities = p.parent.Communities()
-				for _, c := range communities {
-					sort.Sort(ordered.ByID(c))
-				}
-				sort.Sort(ordered.BySliceIDs(communities))
-			} else {
-				communities = reduceDirected(g, nil).Communities()
-			}
-			q := Q(p, nil, 1)
 			if math.IsNaN(q) {
-				// Use an equalable flag value in place of NaN.
-				q = math.Inf(-1)
+				// Don't try again for non-connected case.
+				break
 			}
-			levels = append(levels, level{q: q, communities: communities})
 		}
-		if !reflect.DeepEqual(levels, test.wantLevels) {
-			t.Errorf("unexpected level structure:\n\tgot: %v\n\twant:%v", levels, test.wantLevels)
+
+		var qs []float64
+		for p := r; p != nil; p = p.Expanded().(*ReducedDirected) {
+			qs = append(qs, Q(p, nil, 1))
 		}
+
+		// Recovery of Q values is reversed.
+		if reverse(qs); !sort.Float64sAreSorted(qs) {
+			t.Errorf("Q values not monotonically increasing: %.5v", qs)
+		}
+	}
+
+	gotCommunities := got.Communities()
+	for _, c := range gotCommunities {
+		sort.Sort(ordered.ByID(c))
+	}
+	sort.Sort(ordered.BySliceIDs(gotCommunities))
+	if !reflect.DeepEqual(gotCommunities, want) {
+		t.Errorf("unexpected community membership for %s Q=%.4v:\n\tgot: %v\n\twant:%v",
+			test.name, bestQ, gotCommunities, want)
+		return
+	}
+
+	var levels []level
+	for p := got; p != nil; p = p.Expanded().(*ReducedDirected) {
+		var communities [][]graph.Node
+		if p.parent != nil {
+			communities = p.parent.Communities()
+			for _, c := range communities {
+				sort.Sort(ordered.ByID(c))
+			}
+			sort.Sort(ordered.BySliceIDs(communities))
+		} else {
+			communities = reduceDirected(g, nil).Communities()
+		}
+		q := Q(p, nil, 1)
+		if math.IsNaN(q) {
+			// Use an equalable flag value in place of NaN.
+			q = math.Inf(-1)
+		}
+		levels = append(levels, level{q: q, communities: communities})
+	}
+	if !reflect.DeepEqual(levels, test.wantLevels) {
+		t.Errorf("unexpected level structure:\n\tgot: %v\n\twant:%v", levels, test.wantLevels)
 	}
 }
 
 func TestNonContiguousDirected(t *testing.T) {
-	g := simple.NewDirectedGraph(0, 0)
+	g := simple.NewDirectedGraph()
+	for _, e := range []simple.Edge{
+		{F: simple.Node(0), T: simple.Node(1)},
+		{F: simple.Node(4), T: simple.Node(5)},
+	} {
+		g.SetEdge(e)
+	}
+
+	func() {
+		defer func() {
+			r := recover()
+			if r != nil {
+				t.Error("unexpected panic with non-contiguous ID range")
+			}
+		}()
+		Modularize(g, 1, nil)
+	}()
+}
+
+func TestNonContiguousWeightedDirected(t *testing.T) {
+	g := simple.NewWeightedDirectedGraph(0, 0)
 	for _, e := range []simple.Edge{
 		{F: simple.Node(0), T: simple.Node(1), W: 1},
 		{F: simple.Node(4), T: simple.Node(5), W: 1},
 	} {
-		g.SetEdge(e)
+		g.SetWeightedEdge(e)
 	}
 
 	func() {
diff --git a/graph/community/louvain_test.go b/graph/community/louvain_test.go
index 7ef6c045..32631404 100644
--- a/graph/community/louvain_test.go
+++ b/graph/community/louvain_test.go
@@ -229,8 +229,8 @@ func hasNegative(f []float64) bool {
 }
 
 var (
-	dupGraph         = simple.NewUndirectedGraph(0, 0)
-	dupGraphDirected = simple.NewDirectedGraph(0, 0)
+	dupGraph         = simple.NewUndirectedGraph()
+	dupGraphDirected = simple.NewDirectedGraph()
 )
 
 func init() {
diff --git a/graph/community/louvain_undirected_multiplex_test.go b/graph/community/louvain_undirected_multiplex_test.go
index 769e776b..bef41c14 100644
--- a/graph/community/louvain_undirected_multiplex_test.go
+++ b/graph/community/louvain_undirected_multiplex_test.go
@@ -616,12 +616,32 @@ func TestLouvainMultiplex(t *testing.T) {
 }
 
 func TestNonContiguousUndirectedMultiplex(t *testing.T) {
-	g := simple.NewUndirectedGraph(0, 0)
+	g := simple.NewUndirectedGraph()
+	for _, e := range []simple.Edge{
+		{F: simple.Node(0), T: simple.Node(1)},
+		{F: simple.Node(4), T: simple.Node(5)},
+	} {
+		g.SetEdge(e)
+	}
+
+	func() {
+		defer func() {
+			r := recover()
+			if r != nil {
+				t.Error("unexpected panic with non-contiguous ID range")
+			}
+		}()
+		ModularizeMultiplex(UndirectedLayers{g}, nil, nil, true, nil)
+	}()
+}
+
+func TestNonContiguousWeightedUndirectedMultiplex(t *testing.T) {
+	g := simple.NewWeightedUndirectedGraph(0, 0)
 	for _, e := range []simple.Edge{
 		{F: simple.Node(0), T: simple.Node(1), W: 1},
 		{F: simple.Node(4), T: simple.Node(5), W: 1},
 	} {
-		g.SetEdge(e)
+		g.SetWeightedEdge(e)
 	}
 
 	func() {
@@ -646,7 +666,7 @@ func undirectedMultiplexFrom(raw []layer) (UndirectedLayers, []float64, error) {
 	var layers []graph.Undirected
 	var weights []float64
 	for _, l := range raw {
-		g := simple.NewUndirectedGraph(0, 0)
+		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)) {
@@ -657,7 +677,7 @@ func undirectedMultiplexFrom(raw []layer) (UndirectedLayers, []float64, error) {
 				if l.edgeWeight != 0 {
 					w = l.edgeWeight
 				}
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: w})
+				g.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: w})
 			}
 		}
 		layers = append(layers, g)
diff --git a/graph/community/louvain_undirected_test.go b/graph/community/louvain_undirected_test.go
index 1cf46c4e..6aa7f8ac 100644
--- a/graph/community/louvain_undirected_test.go
+++ b/graph/community/louvain_undirected_test.go
@@ -17,13 +17,15 @@ import (
 	"gonum.org/v1/gonum/graph/simple"
 )
 
-var communityUndirectedQTests = []struct {
+type communityUndirectedQTest struct {
 	name       string
 	g          []intset
 	structures []structure
 
 	wantLevels []level
-}{
+}
+
+var communityUndirectedQTests = []communityUndirectedQTest{
 	// The java reference implementation is available from http://www.ludowaltman.nl/slm/.
 	{
 		name: "unconnected",
@@ -258,194 +260,258 @@ var communityUndirectedQTests = []struct {
 
 func TestCommunityQUndirected(t *testing.T) {
 	for _, test := range communityUndirectedQTests {
-		g := simple.NewUndirectedGraph(0, 0)
+		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
 			}
 		}
-		for _, structure := range test.structures {
-			communities := make([][]graph.Node, len(structure.memberships))
-			for i, c := range structure.memberships {
-				for n := range c {
-					communities[i] = append(communities[i], simple.Node(n))
-				}
+
+		testCommunityQUndirected(t, test, g)
+	}
+}
+
+func TestCommunityQWeightedUndirected(t *testing.T) {
+	for _, test := range communityUndirectedQTests {
+		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)) {
+				g.AddNode(simple.Node(u))
 			}
-			got := Q(g, communities, structure.resolution)
-			if !floats.EqualWithinAbsOrRel(got, structure.want, structure.tol, structure.tol) && !math.IsNaN(structure.want) {
-				for _, c := range communities {
-					sort.Sort(ordered.ByID(c))
-				}
-				t.Errorf("unexpected Q value for %q %v: got: %v want: %v",
-					test.name, communities, got, structure.want)
+			for v := range e {
+				g.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
 			}
 		}
+
+		testCommunityQUndirected(t, test, g)
+	}
+}
+
+func testCommunityQUndirected(t *testing.T, test communityUndirectedQTest, g graph.Undirected) {
+	for _, structure := range test.structures {
+		communities := make([][]graph.Node, len(structure.memberships))
+		for i, c := range structure.memberships {
+			for n := range c {
+				communities[i] = append(communities[i], simple.Node(n))
+			}
+		}
+		got := Q(g, communities, structure.resolution)
+		if !floats.EqualWithinAbsOrRel(got, structure.want, structure.tol, structure.tol) && !math.IsNaN(structure.want) {
+			for _, c := range communities {
+				sort.Sort(ordered.ByID(c))
+			}
+			t.Errorf("unexpected Q value for %q %v: got: %v want: %v",
+				test.name, communities, got, structure.want)
+		}
 	}
 }
 
 func TestCommunityDeltaQUndirected(t *testing.T) {
-tests:
 	for _, test := range communityUndirectedQTests {
-		g := simple.NewUndirectedGraph(0, 0)
+		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
 			}
 		}
 
-		rnd := rand.New(rand.NewSource(1)).Intn
-		for _, structure := range test.structures {
-			communityOf := make(map[int64]int)
-			communities := make([][]graph.Node, len(structure.memberships))
+		testCommunityDeltaQUndirected(t, test, g)
+	}
+}
+
+func TestCommunityDeltaQWeightedUndirected(t *testing.T) {
+	for _, test := range communityUndirectedQTests {
+		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)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
+
+		testCommunityDeltaQUndirected(t, test, g)
+	}
+}
+
+func testCommunityDeltaQUndirected(t *testing.T, test communityUndirectedQTest, g graph.Undirected) {
+	rnd := rand.New(rand.NewSource(1)).Intn
+	for _, structure := range test.structures {
+		communityOf := make(map[int64]int)
+		communities := make([][]graph.Node, len(structure.memberships))
+		for i, c := range structure.memberships {
+			for n := range c {
+				n := int64(n)
+				communityOf[n] = i
+				communities[i] = append(communities[i], simple.Node(n))
+			}
+			sort.Sort(ordered.ByID(communities[i]))
+		}
+
+		before := Q(g, communities, structure.resolution)
+
+		l := newUndirectedLocalMover(reduceUndirected(g, nil), communities, structure.resolution)
+		if l == nil {
+			if !math.IsNaN(before) {
+				t.Errorf("unexpected nil localMover with non-NaN Q graph: Q=%.4v", before)
+			}
+			return
+		}
+
+		// This is done to avoid run-to-run
+		// variation due to map iteration order.
+		sort.Sort(ordered.ByID(l.nodes))
+
+		l.shuffle(rnd)
+
+		for _, target := range l.nodes {
+			got, gotDst, gotSrc := l.deltaQ(target)
+
+			want, wantDst := math.Inf(-1), -1
+			migrated := make([][]graph.Node, len(structure.memberships))
 			for i, c := range structure.memberships {
 				for n := range c {
 					n := int64(n)
-					communityOf[n] = i
-					communities[i] = append(communities[i], simple.Node(n))
-				}
-				sort.Sort(ordered.ByID(communities[i]))
-			}
-
-			before := Q(g, communities, structure.resolution)
-
-			l := newUndirectedLocalMover(reduceUndirected(g, nil), communities, structure.resolution)
-			if l == nil {
-				if !math.IsNaN(before) {
-					t.Errorf("unexpected nil localMover with non-NaN Q graph: Q=%.4v", before)
-				}
-				continue tests
-			}
-
-			// This is done to avoid run-to-run
-			// variation due to map iteration order.
-			sort.Sort(ordered.ByID(l.nodes))
-
-			l.shuffle(rnd)
-
-			for _, target := range l.nodes {
-				got, gotDst, gotSrc := l.deltaQ(target)
-
-				want, wantDst := math.Inf(-1), -1
-				migrated := make([][]graph.Node, len(structure.memberships))
-				for i, c := range structure.memberships {
-					for n := range c {
-						n := int64(n)
-						if n == target.ID() {
-							continue
-						}
-						migrated[i] = append(migrated[i], simple.Node(n))
-					}
-					sort.Sort(ordered.ByID(migrated[i]))
-				}
-
-				for i, c := range structure.memberships {
-					if i == communityOf[target.ID()] {
+					if n == target.ID() {
 						continue
 					}
-					connected := false
-					for n := range c {
-						if g.HasEdgeBetween(simple.Node(n), target) {
-							connected = true
-							break
-						}
-					}
-					if !connected {
-						continue
-					}
-					migrated[i] = append(migrated[i], target)
-					after := Q(g, migrated, structure.resolution)
-					migrated[i] = migrated[i][:len(migrated[i])-1]
-					if after-before > want {
-						want = after - before
-						wantDst = i
-					}
+					migrated[i] = append(migrated[i], simple.Node(n))
 				}
+				sort.Sort(ordered.ByID(migrated[i]))
+			}
 
-				if !floats.EqualWithinAbsOrRel(got, want, structure.tol, structure.tol) || gotDst != wantDst {
-					t.Errorf("unexpected result moving n=%d in c=%d of %s/%.4v: got: %.4v,%d want: %.4v,%d"+
-						"\n\t%v\n\t%v",
-						target.ID(), communityOf[target.ID()], test.name, structure.resolution, got, gotDst, want, wantDst,
-						communities, migrated)
+			for i, c := range structure.memberships {
+				if i == communityOf[target.ID()] {
+					continue
 				}
-				if gotSrc.community != communityOf[target.ID()] {
-					t.Errorf("unexpected source community index: got: %d want: %d", gotSrc, communityOf[target.ID()])
-				} else if communities[gotSrc.community][gotSrc.node].ID() != target.ID() {
-					wantNodeIdx := -1
-					for i, n := range communities[gotSrc.community] {
-						if n.ID() == target.ID() {
-							wantNodeIdx = i
-							break
-						}
+				connected := false
+				for n := range c {
+					if g.HasEdgeBetween(simple.Node(n), target) {
+						connected = true
+						break
 					}
-					t.Errorf("unexpected source node index: got: %d want: %d", gotSrc.node, wantNodeIdx)
 				}
+				if !connected {
+					continue
+				}
+				migrated[i] = append(migrated[i], target)
+				after := Q(g, migrated, structure.resolution)
+				migrated[i] = migrated[i][:len(migrated[i])-1]
+				if after-before > want {
+					want = after - before
+					wantDst = i
+				}
+			}
+
+			if !floats.EqualWithinAbsOrRel(got, want, structure.tol, structure.tol) || gotDst != wantDst {
+				t.Errorf("unexpected result moving n=%d in c=%d of %s/%.4v: got: %.4v,%d want: %.4v,%d"+
+					"\n\t%v\n\t%v",
+					target.ID(), communityOf[target.ID()], test.name, structure.resolution, got, gotDst, want, wantDst,
+					communities, migrated)
+			}
+			if gotSrc.community != communityOf[target.ID()] {
+				t.Errorf("unexpected source community index: got: %d want: %d", gotSrc, communityOf[target.ID()])
+			} else if communities[gotSrc.community][gotSrc.node].ID() != target.ID() {
+				wantNodeIdx := -1
+				for i, n := range communities[gotSrc.community] {
+					if n.ID() == target.ID() {
+						wantNodeIdx = i
+						break
+					}
+				}
+				t.Errorf("unexpected source node index: got: %d want: %d", gotSrc.node, wantNodeIdx)
 			}
 		}
 	}
 }
 
 func TestReduceQConsistencyUndirected(t *testing.T) {
-tests:
 	for _, test := range communityUndirectedQTests {
-		g := simple.NewUndirectedGraph(0, 0)
+		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
 			}
 		}
 
-		for _, structure := range test.structures {
-			if math.IsNaN(structure.want) {
-				continue tests
-			}
+		testReduceQConsistencyUndirected(t, test, g)
+	}
+}
 
-			communities := make([][]graph.Node, len(structure.memberships))
-			for i, c := range structure.memberships {
-				for n := range c {
-					communities[i] = append(communities[i], simple.Node(n))
-				}
-				sort.Sort(ordered.ByID(communities[i]))
+func TestReduceQConsistencyWeightedUndirected(t *testing.T) {
+	for _, test := range communityUndirectedQTests {
+		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)) {
+				g.AddNode(simple.Node(u))
 			}
+			for v := range e {
+				g.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
 
-			gQ := Q(g, communities, structure.resolution)
-			gQnull := Q(g, nil, 1)
+		testReduceQConsistencyUndirected(t, test, g)
+	}
+}
 
-			cg0 := reduceUndirected(g, nil)
-			cg0Qnull := Q(cg0, cg0.Structure(), 1)
-			if !floats.EqualWithinAbsOrRel(gQnull, cg0Qnull, structure.tol, structure.tol) {
-				t.Errorf("disagreement between null Q from method: %v and function: %v", cg0Qnull, gQnull)
-			}
-			cg0Q := Q(cg0, communities, structure.resolution)
-			if !floats.EqualWithinAbsOrRel(gQ, cg0Q, structure.tol, structure.tol) {
-				t.Errorf("unexpected Q result after initial reduction: got: %v want :%v", cg0Q, gQ)
-			}
+func testReduceQConsistencyUndirected(t *testing.T, test communityUndirectedQTest, g graph.Undirected) {
+	for _, structure := range test.structures {
+		if math.IsNaN(structure.want) {
+			return
+		}
 
-			cg1 := reduceUndirected(cg0, communities)
-			cg1Q := Q(cg1, cg1.Structure(), structure.resolution)
-			if !floats.EqualWithinAbsOrRel(gQ, cg1Q, structure.tol, structure.tol) {
-				t.Errorf("unexpected Q result after second reduction: got: %v want :%v", cg1Q, gQ)
+		communities := make([][]graph.Node, len(structure.memberships))
+		for i, c := range structure.memberships {
+			for n := range c {
+				communities[i] = append(communities[i], simple.Node(n))
 			}
+			sort.Sort(ordered.ByID(communities[i]))
+		}
+
+		gQ := Q(g, communities, structure.resolution)
+		gQnull := Q(g, nil, 1)
+
+		cg0 := reduceUndirected(g, nil)
+		cg0Qnull := Q(cg0, cg0.Structure(), 1)
+		if !floats.EqualWithinAbsOrRel(gQnull, cg0Qnull, structure.tol, structure.tol) {
+			t.Errorf("disagreement between null Q from method: %v and function: %v", cg0Qnull, gQnull)
+		}
+		cg0Q := Q(cg0, communities, structure.resolution)
+		if !floats.EqualWithinAbsOrRel(gQ, cg0Q, structure.tol, structure.tol) {
+			t.Errorf("unexpected Q result after initial reduction: got: %v want :%v", cg0Q, gQ)
+		}
+
+		cg1 := reduceUndirected(cg0, communities)
+		cg1Q := Q(cg1, cg1.Structure(), structure.resolution)
+		if !floats.EqualWithinAbsOrRel(gQ, cg1Q, structure.tol, structure.tol) {
+			t.Errorf("unexpected Q result after second reduction: got: %v want :%v", cg1Q, gQ)
 		}
 	}
 }
 
-var localUndirectedMoveTests = []struct {
+type localUndirectedMoveTest struct {
 	name       string
 	g          []intset
 	structures []moveStructures
-}{
+}
+
+var localUndirectedMoveTests = []localUndirectedMoveTest{
 	{
 		name: "blondel",
 		g:    blondel,
@@ -490,39 +556,60 @@ var localUndirectedMoveTests = []struct {
 
 func TestMoveLocalUndirected(t *testing.T) {
 	for _, test := range localUndirectedMoveTests {
-		g := simple.NewUndirectedGraph(0, 0)
+		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
 			}
 		}
 
-		for _, structure := range test.structures {
-			communities := make([][]graph.Node, len(structure.memberships))
-			for i, c := range structure.memberships {
-				for n := range c {
-					communities[i] = append(communities[i], simple.Node(n))
-				}
-				sort.Sort(ordered.ByID(communities[i]))
+		testMoveLocalUndirected(t, test, g)
+	}
+}
+
+func TestMoveLocalWeightedUndirected(t *testing.T) {
+	for _, test := range localUndirectedMoveTests {
+		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)) {
+				g.AddNode(simple.Node(u))
 			}
+			for v := range e {
+				g.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
 
-			r := reduceUndirected(reduceUndirected(g, nil), communities)
+		testMoveLocalUndirected(t, test, g)
+	}
+}
 
-			l := newUndirectedLocalMover(r, r.communities, structure.resolution)
-			for _, n := range structure.targetNodes {
-				dQ, dst, src := l.deltaQ(n)
-				if dQ > 0 {
-					before := Q(r, l.communities, structure.resolution)
-					l.move(dst, src)
-					after := Q(r, l.communities, structure.resolution)
-					want := after - before
-					if !floats.EqualWithinAbsOrRel(dQ, want, structure.tol, structure.tol) {
-						t.Errorf("unexpected deltaQ: got: %v want: %v", dQ, want)
-					}
+func testMoveLocalUndirected(t *testing.T, test localUndirectedMoveTest, g graph.Undirected) {
+	for _, structure := range test.structures {
+		communities := make([][]graph.Node, len(structure.memberships))
+		for i, c := range structure.memberships {
+			for n := range c {
+				communities[i] = append(communities[i], simple.Node(n))
+			}
+			sort.Sort(ordered.ByID(communities[i]))
+		}
+
+		r := reduceUndirected(reduceUndirected(g, nil), communities)
+
+		l := newUndirectedLocalMover(r, r.communities, structure.resolution)
+		for _, n := range structure.targetNodes {
+			dQ, dst, src := l.deltaQ(n)
+			if dQ > 0 {
+				before := Q(r, l.communities, structure.resolution)
+				l.move(dst, src)
+				after := Q(r, l.communities, structure.resolution)
+				want := after - before
+				if !floats.EqualWithinAbsOrRel(dQ, want, structure.tol, structure.tol) {
+					t.Errorf("unexpected deltaQ: got: %v want: %v", dQ, want)
 				}
 			}
 		}
@@ -530,105 +617,146 @@ func TestMoveLocalUndirected(t *testing.T) {
 }
 
 func TestModularizeUndirected(t *testing.T) {
-	const louvainIterations = 20
-
 	for _, test := range communityUndirectedQTests {
-		g := simple.NewUndirectedGraph(0, 0)
+		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
 			}
 		}
 
-		if test.structures[0].resolution != 1 {
-			panic("bad test: expect resolution=1")
-		}
-		want := make([][]graph.Node, len(test.structures[0].memberships))
-		for i, c := range test.structures[0].memberships {
-			for n := range c {
-				want[i] = append(want[i], simple.Node(n))
+		testModularizeUndirected(t, test, g)
+	}
+}
+
+func TestModularizeWeightedUndirected(t *testing.T) {
+	for _, test := range communityUndirectedQTests {
+		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)) {
+				g.AddNode(simple.Node(u))
 			}
-			sort.Sort(ordered.ByID(want[i]))
-		}
-		sort.Sort(ordered.BySliceIDs(want))
-
-		var (
-			got   *ReducedUndirected
-			bestQ = math.Inf(-1)
-		)
-		// Modularize is randomised so we do this to
-		// ensure the level tests are consistent.
-		src := rand.New(rand.NewSource(1))
-		for i := 0; i < louvainIterations; i++ {
-			r := Modularize(g, 1, src).(*ReducedUndirected)
-			if q := Q(r, nil, 1); q > bestQ || math.IsNaN(q) {
-				bestQ = q
-				got = r
-
-				if math.IsNaN(q) {
-					// Don't try again for non-connected case.
-					break
-				}
-			}
-
-			var qs []float64
-			for p := r; p != nil; p = p.Expanded().(*ReducedUndirected) {
-				qs = append(qs, Q(p, nil, 1))
-			}
-
-			// Recovery of Q values is reversed.
-			if reverse(qs); !sort.Float64sAreSorted(qs) {
-				t.Errorf("Q values not monotonically increasing: %.5v", qs)
+			for v := range e {
+				g.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
 			}
 		}
 
-		gotCommunities := got.Communities()
-		for _, c := range gotCommunities {
-			sort.Sort(ordered.ByID(c))
-		}
-		sort.Sort(ordered.BySliceIDs(gotCommunities))
-		if !reflect.DeepEqual(gotCommunities, want) {
-			t.Errorf("unexpected community membership for %s Q=%.4v:\n\tgot: %v\n\twant:%v",
-				test.name, bestQ, gotCommunities, want)
-			continue
-		}
+		testModularizeUndirected(t, test, g)
+	}
+}
+
+func testModularizeUndirected(t *testing.T, test communityUndirectedQTest, g graph.Undirected) {
+	const louvainIterations = 20
+
+	if test.structures[0].resolution != 1 {
+		panic("bad test: expect resolution=1")
+	}
+	want := make([][]graph.Node, len(test.structures[0].memberships))
+	for i, c := range test.structures[0].memberships {
+		for n := range c {
+			want[i] = append(want[i], simple.Node(n))
+		}
+		sort.Sort(ordered.ByID(want[i]))
+	}
+	sort.Sort(ordered.BySliceIDs(want))
+
+	var (
+		got   *ReducedUndirected
+		bestQ = math.Inf(-1)
+	)
+	// Modularize is randomised so we do this to
+	// ensure the level tests are consistent.
+	src := rand.New(rand.NewSource(1))
+	for i := 0; i < louvainIterations; i++ {
+		r := Modularize(g, 1, src).(*ReducedUndirected)
+		if q := Q(r, nil, 1); q > bestQ || math.IsNaN(q) {
+			bestQ = q
+			got = r
 
-		var levels []level
-		for p := got; p != nil; p = p.Expanded().(*ReducedUndirected) {
-			var communities [][]graph.Node
-			if p.parent != nil {
-				communities = p.parent.Communities()
-				for _, c := range communities {
-					sort.Sort(ordered.ByID(c))
-				}
-				sort.Sort(ordered.BySliceIDs(communities))
-			} else {
-				communities = reduceUndirected(g, nil).Communities()
-			}
-			q := Q(p, nil, 1)
 			if math.IsNaN(q) {
-				// Use an equalable flag value in place of NaN.
-				q = math.Inf(-1)
+				// Don't try again for non-connected case.
+				break
 			}
-			levels = append(levels, level{q: q, communities: communities})
 		}
-		if !reflect.DeepEqual(levels, test.wantLevels) {
-			t.Errorf("unexpected level structure:\n\tgot: %v\n\twant:%v", levels, test.wantLevels)
+
+		var qs []float64
+		for p := r; p != nil; p = p.Expanded().(*ReducedUndirected) {
+			qs = append(qs, Q(p, nil, 1))
 		}
+
+		// Recovery of Q values is reversed.
+		if reverse(qs); !sort.Float64sAreSorted(qs) {
+			t.Errorf("Q values not monotonically increasing: %.5v", qs)
+		}
+	}
+
+	gotCommunities := got.Communities()
+	for _, c := range gotCommunities {
+		sort.Sort(ordered.ByID(c))
+	}
+	sort.Sort(ordered.BySliceIDs(gotCommunities))
+	if !reflect.DeepEqual(gotCommunities, want) {
+		t.Errorf("unexpected community membership for %s Q=%.4v:\n\tgot: %v\n\twant:%v",
+			test.name, bestQ, gotCommunities, want)
+		return
+	}
+
+	var levels []level
+	for p := got; p != nil; p = p.Expanded().(*ReducedUndirected) {
+		var communities [][]graph.Node
+		if p.parent != nil {
+			communities = p.parent.Communities()
+			for _, c := range communities {
+				sort.Sort(ordered.ByID(c))
+			}
+			sort.Sort(ordered.BySliceIDs(communities))
+		} else {
+			communities = reduceUndirected(g, nil).Communities()
+		}
+		q := Q(p, nil, 1)
+		if math.IsNaN(q) {
+			// Use an equalable flag value in place of NaN.
+			q = math.Inf(-1)
+		}
+		levels = append(levels, level{q: q, communities: communities})
+	}
+	if !reflect.DeepEqual(levels, test.wantLevels) {
+		t.Errorf("unexpected level structure:\n\tgot: %v\n\twant:%v", levels, test.wantLevels)
 	}
 }
 
 func TestNonContiguousUndirected(t *testing.T) {
-	g := simple.NewUndirectedGraph(0, 0)
+	g := simple.NewUndirectedGraph()
+	for _, e := range []simple.Edge{
+		{F: simple.Node(0), T: simple.Node(1)},
+		{F: simple.Node(4), T: simple.Node(5)},
+	} {
+		g.SetEdge(e)
+	}
+
+	func() {
+		defer func() {
+			r := recover()
+			if r != nil {
+				t.Error("unexpected panic with non-contiguous ID range")
+			}
+		}()
+		Modularize(g, 1, nil)
+	}()
+}
+
+func TestNonContiguousWeightedUndirected(t *testing.T) {
+	g := simple.NewWeightedUndirectedGraph(0, 0)
 	for _, e := range []simple.Edge{
 		{F: simple.Node(0), T: simple.Node(1), W: 1},
 		{F: simple.Node(4), T: simple.Node(5), W: 1},
 	} {
-		g.SetEdge(e)
+		g.SetWeightedEdge(e)
 	}
 
 	func() {
diff --git a/graph/encoding/dot/decode_test.go b/graph/encoding/dot/decode_test.go
index 0416ecd4..d05b0507 100644
--- a/graph/encoding/dot/decode_test.go
+++ b/graph/encoding/dot/decode_test.go
@@ -110,7 +110,7 @@ type dotDirectedGraph struct {
 // newDotDirectedGraph returns a new directed capable of creating user-defined
 // nodes and edges.
 func newDotDirectedGraph() *dotDirectedGraph {
-	return &dotDirectedGraph{DirectedGraph: simple.NewDirectedGraph(0, 0)}
+	return &dotDirectedGraph{DirectedGraph: simple.NewDirectedGraph()}
 }
 
 // NewNode returns a new node with a unique node ID for the graph.
@@ -145,7 +145,7 @@ type dotUndirectedGraph struct {
 // newDotUndirectedGraph returns a new undirected capable of creating user-
 // defined nodes and edges.
 func newDotUndirectedGraph() *dotUndirectedGraph {
-	return &dotUndirectedGraph{UndirectedGraph: simple.NewUndirectedGraph(0, 0)}
+	return &dotUndirectedGraph{UndirectedGraph: simple.NewUndirectedGraph()}
 }
 
 // NewNode adds a new node with a unique node ID to the graph.
diff --git a/graph/encoding/dot/encode_test.go b/graph/encoding/dot/encode_test.go
index 0e94291c..d4dba18c 100644
--- a/graph/encoding/dot/encode_test.go
+++ b/graph/encoding/dot/encode_test.go
@@ -5,7 +5,6 @@
 package dot
 
 import (
-	"math"
 	"testing"
 
 	"gonum.org/v1/gonum/graph"
@@ -55,7 +54,7 @@ var (
 )
 
 func directedGraphFrom(g []intset) graph.Directed {
-	dg := simple.NewDirectedGraph(0, math.Inf(1))
+	dg := simple.NewDirectedGraph()
 	for u, e := range g {
 		for v := range e {
 			dg.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
@@ -65,7 +64,7 @@ func directedGraphFrom(g []intset) graph.Directed {
 }
 
 func undirectedGraphFrom(g []intset) graph.Graph {
-	dg := simple.NewUndirectedGraph(0, math.Inf(1))
+	dg := simple.NewUndirectedGraph()
 	for u, e := range g {
 		for v := range e {
 			dg.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
@@ -85,7 +84,7 @@ func (n namedNode) ID() int64     { return n.id }
 func (n namedNode) DOTID() string { return n.name }
 
 func directedNamedIDGraphFrom(g []intset) graph.Directed {
-	dg := simple.NewDirectedGraph(0, math.Inf(1))
+	dg := simple.NewDirectedGraph()
 	for u, e := range g {
 		u := int64(u)
 		nu := namedNode{id: u, name: alpha[u : u+1]}
@@ -98,7 +97,7 @@ func directedNamedIDGraphFrom(g []intset) graph.Directed {
 }
 
 func undirectedNamedIDGraphFrom(g []intset) graph.Graph {
-	dg := simple.NewUndirectedGraph(0, math.Inf(1))
+	dg := simple.NewUndirectedGraph()
 	for u, e := range g {
 		u := int64(u)
 		nu := namedNode{id: u, name: alpha[u : u+1]}
@@ -120,7 +119,7 @@ func (n attrNode) ID() int64                        { return n.id }
 func (n attrNode) Attributes() []encoding.Attribute { return n.attr }
 
 func directedNodeAttrGraphFrom(g []intset, attr [][]encoding.Attribute) graph.Directed {
-	dg := simple.NewDirectedGraph(0, math.Inf(1))
+	dg := simple.NewDirectedGraph()
 	for u, e := range g {
 		u := int64(u)
 		var at []encoding.Attribute
@@ -140,7 +139,7 @@ func directedNodeAttrGraphFrom(g []intset, attr [][]encoding.Attribute) graph.Di
 }
 
 func undirectedNodeAttrGraphFrom(g []intset, attr [][]encoding.Attribute) graph.Graph {
-	dg := simple.NewUndirectedGraph(0, math.Inf(1))
+	dg := simple.NewUndirectedGraph()
 	for u, e := range g {
 		u := int64(u)
 		var at []encoding.Attribute
@@ -170,7 +169,7 @@ func (n namedAttrNode) DOTID() string                    { return n.name }
 func (n namedAttrNode) Attributes() []encoding.Attribute { return n.attr }
 
 func directedNamedIDNodeAttrGraphFrom(g []intset, attr [][]encoding.Attribute) graph.Directed {
-	dg := simple.NewDirectedGraph(0, math.Inf(1))
+	dg := simple.NewDirectedGraph()
 	for u, e := range g {
 		u := int64(u)
 		var at []encoding.Attribute
@@ -190,7 +189,7 @@ func directedNamedIDNodeAttrGraphFrom(g []intset, attr [][]encoding.Attribute) g
 }
 
 func undirectedNamedIDNodeAttrGraphFrom(g []intset, attr [][]encoding.Attribute) graph.Graph {
-	dg := simple.NewUndirectedGraph(0, math.Inf(1))
+	dg := simple.NewUndirectedGraph()
 	for u, e := range g {
 		u := int64(u)
 		var at []encoding.Attribute
@@ -221,7 +220,7 @@ func (e attrEdge) Weight() float64                  { return 0 }
 func (e attrEdge) Attributes() []encoding.Attribute { return e.attr }
 
 func directedEdgeAttrGraphFrom(g []intset, attr map[edge][]encoding.Attribute) graph.Directed {
-	dg := simple.NewDirectedGraph(0, math.Inf(1))
+	dg := simple.NewDirectedGraph()
 	for u, e := range g {
 		u := int64(u)
 		for v := range e {
@@ -232,7 +231,7 @@ func directedEdgeAttrGraphFrom(g []intset, attr map[edge][]encoding.Attribute) g
 }
 
 func undirectedEdgeAttrGraphFrom(g []intset, attr map[edge][]encoding.Attribute) graph.Graph {
-	dg := simple.NewUndirectedGraph(0, math.Inf(1))
+	dg := simple.NewUndirectedGraph()
 	for u, e := range g {
 		u := int64(u)
 		for v := range e {
@@ -273,7 +272,7 @@ func (e portedEdge) ToPort() (port, compass string) {
 }
 
 func directedPortedAttrGraphFrom(g []intset, attr [][]encoding.Attribute, ports map[edge]portedEdge) graph.Directed {
-	dg := simple.NewDirectedGraph(0, math.Inf(1))
+	dg := simple.NewDirectedGraph()
 	for u, e := range g {
 		u := int64(u)
 		var at []encoding.Attribute
@@ -295,7 +294,7 @@ func directedPortedAttrGraphFrom(g []intset, attr [][]encoding.Attribute, ports
 }
 
 func undirectedPortedAttrGraphFrom(g []intset, attr [][]encoding.Attribute, ports map[edge]portedEdge) graph.Graph {
-	dg := simple.NewUndirectedGraph(0, math.Inf(1))
+	dg := simple.NewUndirectedGraph()
 	for u, e := range g {
 		u := int64(u)
 		var at []encoding.Attribute
@@ -337,10 +336,10 @@ type structuredGraph struct {
 }
 
 func undirectedStructuredGraphFrom(c []edge, g ...[]intset) graph.Graph {
-	s := &structuredGraph{UndirectedGraph: simple.NewUndirectedGraph(0, math.Inf(1))}
+	s := &structuredGraph{UndirectedGraph: simple.NewUndirectedGraph()}
 	var base int64
 	for i, sg := range g {
-		sub := simple.NewUndirectedGraph(0, math.Inf(1))
+		sub := simple.NewUndirectedGraph()
 		for u, e := range sg {
 			u := int64(u)
 			for v := range e {
@@ -382,7 +381,7 @@ func undirectedSubGraphFrom(g []intset, s map[int64][]intset) graph.Graph {
 	var base int64
 	subs := make(map[int64]subGraph)
 	for i, sg := range s {
-		sub := simple.NewUndirectedGraph(0, math.Inf(1))
+		sub := simple.NewUndirectedGraph()
 		for u, e := range sg {
 			u := int64(u)
 			for v := range e {
@@ -394,7 +393,7 @@ func undirectedSubGraphFrom(g []intset, s map[int64][]intset) graph.Graph {
 		base += int64(len(sg))
 	}
 
-	dg := simple.NewUndirectedGraph(0, math.Inf(1))
+	dg := simple.NewUndirectedGraph()
 	for u, e := range g {
 		u := int64(u)
 		var nu graph.Node
diff --git a/graph/encoding/graphql/decode_test.go b/graph/encoding/graphql/decode_test.go
index 84ba00d8..4bcc7925 100644
--- a/graph/encoding/graphql/decode_test.go
+++ b/graph/encoding/graphql/decode_test.go
@@ -155,7 +155,7 @@ type directedGraph struct {
 }
 
 func newDirectedGraph() *directedGraph {
-	return &directedGraph{DirectedGraph: simple.NewDirectedGraph(0, 0)}
+	return &directedGraph{DirectedGraph: simple.NewDirectedGraph()}
 }
 
 func (g *directedGraph) NewNode() graph.Node {
diff --git a/graph/graph.go b/graph/graph.go
index 50750b6a..0ca587d8 100644
--- a/graph/graph.go
+++ b/graph/graph.go
@@ -15,13 +15,15 @@ type Node interface {
 type Edge interface {
 	From() Node
 	To() Node
-	Weight() float64
 }
 
-// WeightedEdge is a graph edge. In directed graphs, the direction
+// WeightedEdge is a weighted graph edge. In directed graphs, the direction
 // of the edge is given from -> to, otherwise the edge is semantically
 // unordered.
-type WeightedEdge Edge
+type WeightedEdge interface {
+	Edge
+	Weight() float64
+}
 
 // Graph is a generalized graph.
 type Graph interface {
@@ -143,6 +145,22 @@ type EdgeAdder interface {
 	SetEdge(e Edge)
 }
 
+// WeightedEdgeAdder is an interface for adding edges to a graph.
+type WeightedEdgeAdder interface {
+	// NewWeightedEdge returns a new WeightedEdge from
+	// the source to the destination node.
+	NewWeightedEdge(from, to Node, weight float64) WeightedEdge
+
+	// SetWeightedEdge adds an edge from one node to
+	// another. If the graph supports node addition
+	// the nodes will be added if they do not exist,
+	// otherwise SetWeightedEdge will panic.
+	// The behavior of a WeightedEdgeAdder when the IDs
+	// returned by e.From and e.To are equal is
+	// implementation-dependent.
+	SetWeightedEdge(e WeightedEdge)
+}
+
 // EdgeRemover is an interface for removing nodes from a graph.
 type EdgeRemover interface {
 	// RemoveEdge removes the given edge, leaving the
@@ -157,29 +175,42 @@ type Builder interface {
 	EdgeAdder
 }
 
+// WeightedBuilder is a graph that can have nodes and weighted edges added.
+type WeightedBuilder interface {
+	NodeAdder
+	WeightedEdgeAdder
+}
+
 // UndirectedBuilder is an undirected graph builder.
 type UndirectedBuilder interface {
 	Undirected
 	Builder
 }
 
+// UndirectedWeightedBuilder is an undirected weighted graph builder.
+type UndirectedWeightedBuilder interface {
+	Undirected
+	WeightedBuilder
+}
+
 // DirectedBuilder is a directed graph builder.
 type DirectedBuilder interface {
 	Directed
 	Builder
 }
 
+// DirectedWeightedBuilder is a directed weighted graph builder.
+type DirectedWeightedBuilder interface {
+	Directed
+	WeightedBuilder
+}
+
 // Copy copies nodes and edges as undirected edges from the source to the destination
 // without first clearing the destination. Copy will panic if a node ID in the source
 // graph matches a node ID in the destination.
 //
 // If the source is undirected and the destination is directed both directions will
 // be present in the destination after the copy is complete.
-//
-// If the source is a directed graph, the destination is undirected, and a fundamental
-// cycle exists with two nodes where the edge weights differ, the resulting destination
-// graph's edge weight between those nodes is undefined. If there is a defined function
-// to resolve such conflicts, an Undirect may be used to do this.
 func Copy(dst Builder, src Graph) {
 	nodes := src.Nodes()
 	for _, n := range nodes {
@@ -191,3 +222,26 @@ func Copy(dst Builder, src Graph) {
 		}
 	}
 }
+
+// CopyWeighted copies nodes and edges as undirected edges from the source to the destination
+// without first clearing the destination. Copy will panic if a node ID in the source
+// graph matches a node ID in the destination.
+//
+// If the source is undirected and the destination is directed both directions will
+// be present in the destination after the copy is complete.
+//
+// If the source is a directed graph, the destination is undirected, and a fundamental
+// cycle exists with two nodes where the edge weights differ, the resulting destination
+// graph's edge weight between those nodes is undefined. If there is a defined function
+// to resolve such conflicts, an UndirectWeighted may be used to do this.
+func CopyWeighted(dst WeightedBuilder, src Weighted) {
+	nodes := src.Nodes()
+	for _, n := range nodes {
+		dst.AddNode(n)
+	}
+	for _, u := range nodes {
+		for _, v := range src.From(u) {
+			dst.SetWeightedEdge(src.WeightedEdge(u, v))
+		}
+	}
+}
diff --git a/graph/graphs/gen/batagelj_brandes_test.go b/graph/graphs/gen/batagelj_brandes_test.go
index b9993934..544e2e96 100644
--- a/graph/graphs/gen/batagelj_brandes_test.go
+++ b/graph/graphs/gen/batagelj_brandes_test.go
@@ -5,7 +5,6 @@
 package gen
 
 import (
-	"math"
 	"testing"
 
 	"gonum.org/v1/gonum/graph"
@@ -54,7 +53,7 @@ func (g *gnDirected) SetEdge(e graph.Edge) {
 func TestGnpUndirected(t *testing.T) {
 	for n := 2; n <= 20; n++ {
 		for p := 0.; p <= 1; p += 0.1 {
-			g := &gnUndirected{UndirectedBuilder: simple.NewUndirectedGraph(0, math.Inf(1))}
+			g := &gnUndirected{UndirectedBuilder: simple.NewUndirectedGraph()}
 			err := Gnp(g, n, p, nil)
 			if err != nil {
 				t.Fatalf("unexpected error: n=%d, p=%v: %v", n, p, err)
@@ -75,7 +74,7 @@ func TestGnpUndirected(t *testing.T) {
 func TestGnpDirected(t *testing.T) {
 	for n := 2; n <= 20; n++ {
 		for p := 0.; p <= 1; p += 0.1 {
-			g := &gnDirected{DirectedBuilder: simple.NewDirectedGraph(0, math.Inf(1))}
+			g := &gnDirected{DirectedBuilder: simple.NewDirectedGraph()}
 			err := Gnp(g, n, p, nil)
 			if err != nil {
 				t.Fatalf("unexpected error: n=%d, p=%v: %v", n, p, err)
@@ -94,7 +93,7 @@ func TestGnmUndirected(t *testing.T) {
 	for n := 2; n <= 20; n++ {
 		nChoose2 := (n - 1) * n / 2
 		for m := 0; m <= nChoose2; m++ {
-			g := &gnUndirected{UndirectedBuilder: simple.NewUndirectedGraph(0, math.Inf(1))}
+			g := &gnUndirected{UndirectedBuilder: simple.NewUndirectedGraph()}
 			err := Gnm(g, n, m, nil)
 			if err != nil {
 				t.Fatalf("unexpected error: n=%d, m=%d: %v", n, m, err)
@@ -116,7 +115,7 @@ func TestGnmDirected(t *testing.T) {
 	for n := 2; n <= 20; n++ {
 		nChoose2 := (n - 1) * n / 2
 		for m := 0; m <= nChoose2*2; m++ {
-			g := &gnDirected{DirectedBuilder: simple.NewDirectedGraph(0, math.Inf(1))}
+			g := &gnDirected{DirectedBuilder: simple.NewDirectedGraph()}
 			err := Gnm(g, n, m, nil)
 			if err != nil {
 				t.Fatalf("unexpected error: n=%d, m=%d: %v", n, m, err)
@@ -135,7 +134,7 @@ func TestSmallWorldsBBUndirected(t *testing.T) {
 	for n := 2; n <= 20; n++ {
 		for d := 1; d <= (n-1)/2; d++ {
 			for p := 0.; p < 1; p += 0.1 {
-				g := &gnUndirected{UndirectedBuilder: simple.NewUndirectedGraph(0, math.Inf(1))}
+				g := &gnUndirected{UndirectedBuilder: simple.NewUndirectedGraph()}
 				err := SmallWorldsBB(g, n, d, p, nil)
 				if err != nil {
 					t.Fatalf("unexpected error: n=%d, d=%d, p=%v: %v", n, d, p, err)
@@ -158,7 +157,7 @@ func TestSmallWorldsBBDirected(t *testing.T) {
 	for n := 2; n <= 20; n++ {
 		for d := 1; d <= (n-1)/2; d++ {
 			for p := 0.; p < 1; p += 0.1 {
-				g := &gnDirected{DirectedBuilder: simple.NewDirectedGraph(0, math.Inf(1))}
+				g := &gnDirected{DirectedBuilder: simple.NewDirectedGraph()}
 				err := SmallWorldsBB(g, n, d, p, nil)
 				if err != nil {
 					t.Fatalf("unexpected error: n=%d, d=%d, p=%v: %v", n, d, p, err)
diff --git a/graph/graphs/gen/duplication_test.go b/graph/graphs/gen/duplication_test.go
index 56e7d05a..b58eb899 100644
--- a/graph/graphs/gen/duplication_test.go
+++ b/graph/graphs/gen/duplication_test.go
@@ -5,7 +5,6 @@
 package gen
 
 import (
-	"math"
 	"testing"
 
 	"gonum.org/v1/gonum/graph"
@@ -38,7 +37,7 @@ func TestDuplication(t *testing.T) {
 		for alpha := 0.1; alpha <= 1; alpha += 0.1 {
 			for delta := 0.; delta <= 1; delta += 0.2 {
 				for sigma := 0.; sigma <= 1; sigma += 0.2 {
-					g := &duplication{UndirectedMutator: simple.NewUndirectedGraph(0, math.Inf(1))}
+					g := &duplication{UndirectedMutator: simple.NewUndirectedGraph()}
 					err := Duplication(g, n, delta, alpha, sigma, nil)
 					if err != nil {
 						t.Fatalf("unexpected error: n=%d, alpha=%v, delta=%v sigma=%v: %v", n, alpha, delta, sigma, err)
diff --git a/graph/graphs/gen/holme_kim_test.go b/graph/graphs/gen/holme_kim_test.go
index 370c42c7..82eb62a8 100644
--- a/graph/graphs/gen/holme_kim_test.go
+++ b/graph/graphs/gen/holme_kim_test.go
@@ -5,7 +5,6 @@
 package gen
 
 import (
-	"math"
 	"testing"
 
 	"gonum.org/v1/gonum/graph/simple"
@@ -15,7 +14,7 @@ func TestTunableClusteringScaleFree(t *testing.T) {
 	for n := 2; n <= 20; n++ {
 		for m := 0; m < n; m++ {
 			for p := 0.; p <= 1; p += 0.1 {
-				g := &gnUndirected{UndirectedBuilder: simple.NewUndirectedGraph(0, math.Inf(1))}
+				g := &gnUndirected{UndirectedBuilder: simple.NewUndirectedGraph()}
 				err := TunableClusteringScaleFree(g, n, m, p, nil)
 				if err != nil {
 					t.Fatalf("unexpected error: n=%d, m=%d, p=%v: %v", n, m, p, err)
@@ -37,7 +36,7 @@ func TestTunableClusteringScaleFree(t *testing.T) {
 func TestPreferentialAttachment(t *testing.T) {
 	for n := 2; n <= 20; n++ {
 		for m := 0; m < n; m++ {
-			g := &gnUndirected{UndirectedBuilder: simple.NewUndirectedGraph(0, math.Inf(1))}
+			g := &gnUndirected{UndirectedBuilder: simple.NewUndirectedGraph()}
 			err := PreferentialAttachment(g, n, m, nil)
 			if err != nil {
 				t.Fatalf("unexpected error: n=%d, m=%d: %v", n, m, err)
diff --git a/graph/graphs/gen/small_world_test.go b/graph/graphs/gen/small_world_test.go
index dd413a76..ef667146 100644
--- a/graph/graphs/gen/small_world_test.go
+++ b/graph/graphs/gen/small_world_test.go
@@ -5,7 +5,6 @@
 package gen
 
 import (
-	"math"
 	"testing"
 
 	"gonum.org/v1/gonum/graph/simple"
@@ -22,7 +21,7 @@ func TestNavigableSmallWorldUndirected(t *testing.T) {
 		for q := 0; q < 10; q++ {
 			for r := 0.5; r < 10; r++ {
 				for _, dims := range smallWorldDimensionParameters {
-					g := &gnUndirected{UndirectedBuilder: simple.NewUndirectedGraph(0, math.Inf(1))}
+					g := &gnUndirected{UndirectedBuilder: simple.NewUndirectedGraph()}
 					err := NavigableSmallWorld(g, dims, p, q, r, nil)
 					n := 1
 					for _, d := range dims {
@@ -51,7 +50,7 @@ func TestNavigableSmallWorldDirected(t *testing.T) {
 		for q := 0; q < 10; q++ {
 			for r := 0.5; r < 10; r++ {
 				for _, dims := range smallWorldDimensionParameters {
-					g := &gnDirected{DirectedBuilder: simple.NewDirectedGraph(0, math.Inf(1))}
+					g := &gnDirected{DirectedBuilder: simple.NewDirectedGraph()}
 					err := NavigableSmallWorld(g, dims, p, q, r, nil)
 					n := 1
 					for _, d := range dims {
diff --git a/graph/network/betweenness_test.go b/graph/network/betweenness_test.go
index 401b71b1..20c9b4ed 100644
--- a/graph/network/betweenness_test.go
+++ b/graph/network/betweenness_test.go
@@ -176,15 +176,14 @@ var betweennessTests = []struct {
 
 func TestBetweenness(t *testing.T) {
 	for i, test := range betweennessTests {
-		g := simple.NewUndirectedGraph(0, math.Inf(1))
+		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				// Weight omitted to show weight-independence.
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 0})
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
 			}
 		}
 		got := Betweenness(g)
@@ -206,15 +205,14 @@ func TestBetweenness(t *testing.T) {
 
 func TestEdgeBetweenness(t *testing.T) {
 	for i, test := range betweennessTests {
-		g := simple.NewUndirectedGraph(0, math.Inf(1))
+		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				// Weight omitted to show weight-independence.
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 0})
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
 			}
 		}
 		got := EdgeBetweenness(g)
@@ -239,14 +237,14 @@ func TestEdgeBetweenness(t *testing.T) {
 
 func TestBetweennessWeighted(t *testing.T) {
 	for i, test := range betweennessTests {
-		g := simple.NewUndirectedGraph(0, math.Inf(1))
+		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)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+				g.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
 			}
 		}
 
@@ -275,14 +273,14 @@ func TestBetweennessWeighted(t *testing.T) {
 
 func TestEdgeBetweennessWeighted(t *testing.T) {
 	for i, test := range betweennessTests {
-		g := simple.NewUndirectedGraph(0, math.Inf(1))
+		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)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+				g.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
 			}
 		}
 
diff --git a/graph/network/distance_test.go b/graph/network/distance_test.go
index 94778f0a..7e2b1a32 100644
--- a/graph/network/distance_test.go
+++ b/graph/network/distance_test.go
@@ -143,14 +143,14 @@ func TestDistanceCentralityUndirected(t *testing.T) {
 	prec := 1 - int(math.Log10(tol))
 
 	for i, test := range undirectedCentralityTests {
-		g := simple.NewUndirectedGraph(0, math.Inf(1))
+		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)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+				g.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
 			}
 		}
 		p, ok := path.FloydWarshall(g)
@@ -333,14 +333,14 @@ func TestDistanceCentralityDirected(t *testing.T) {
 	prec := 1 - int(math.Log10(tol))
 
 	for i, test := range directedCentralityTests {
-		g := simple.NewDirectedGraph(0, math.Inf(1))
+		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)) {
 				g.AddNode(simple.Node(u))
 			}
 			for v := range e {
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+				g.SetWeightedEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
 			}
 		}
 		p, ok := path.FloydWarshall(g)
diff --git a/graph/network/hits_test.go b/graph/network/hits_test.go
index 4b50685e..b711f36e 100644
--- a/graph/network/hits_test.go
+++ b/graph/network/hits_test.go
@@ -43,7 +43,7 @@ var hitsTests = []struct {
 
 func TestHITS(t *testing.T) {
 	for i, test := range hitsTests {
-		g := simple.NewDirectedGraph(0, math.Inf(1))
+		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
diff --git a/graph/network/page_test.go b/graph/network/page_test.go
index d889c6c8..0a85dcf2 100644
--- a/graph/network/page_test.go
+++ b/graph/network/page_test.go
@@ -81,7 +81,7 @@ var pageRankTests = []struct {
 
 func TestPageRank(t *testing.T) {
 	for i, test := range pageRankTests {
-		g := simple.NewDirectedGraph(0, math.Inf(1))
+		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
@@ -105,7 +105,7 @@ func TestPageRank(t *testing.T) {
 
 func TestPageRankSparse(t *testing.T) {
 	for i, test := range pageRankTests {
-		g := simple.NewDirectedGraph(0, math.Inf(1))
+		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
diff --git a/graph/path/a_star_test.go b/graph/path/a_star_test.go
index 508a8937..3284880d 100644
--- a/graph/path/a_star_test.go
+++ b/graph/path/a_star_test.go
@@ -154,7 +154,7 @@ func TestAStar(t *testing.T) {
 }
 
 func TestExhaustiveAStar(t *testing.T) {
-	g := simple.NewUndirectedGraph(0, math.Inf(1))
+	g := simple.NewWeightedUndirectedGraph(0, math.Inf(1))
 	nodes := []locatedNode{
 		{id: 1, x: 0, y: 6},
 		{id: 2, x: 1, y: 0},
@@ -179,7 +179,7 @@ func TestExhaustiveAStar(t *testing.T) {
 		{from: g.Node(5), to: g.Node(6), cost: 9},
 	}
 	for _, e := range edges {
-		g.SetEdge(e)
+		g.SetWeightedEdge(e)
 	}
 
 	heuristic := func(u, v graph.Node) float64 {
@@ -247,7 +247,7 @@ func TestAStarNullHeuristic(t *testing.T) {
 	for _, test := range testgraphs.ShortestPathTests {
 		g := test.Graph()
 		for _, e := range test.Edges {
-			g.SetEdge(e)
+			g.SetWeightedEdge(e)
 		}
 
 		var (
diff --git a/graph/path/bellman_ford_moore_test.go b/graph/path/bellman_ford_moore_test.go
index 55ebefd4..b753368f 100644
--- a/graph/path/bellman_ford_moore_test.go
+++ b/graph/path/bellman_ford_moore_test.go
@@ -17,7 +17,7 @@ func TestBellmanFordFrom(t *testing.T) {
 	for _, test := range testgraphs.ShortestPathTests {
 		g := test.Graph()
 		for _, e := range test.Edges {
-			g.SetEdge(e)
+			g.SetWeightedEdge(e)
 		}
 
 		pt, ok := BellmanFordFrom(test.Query.From(), g.(graph.Graph))
diff --git a/graph/path/bench_test.go b/graph/path/bench_test.go
index 36279957..e08525f0 100644
--- a/graph/path/bench_test.go
+++ b/graph/path/bench_test.go
@@ -5,7 +5,6 @@
 package path
 
 import (
-	"math"
 	"testing"
 
 	"gonum.org/v1/gonum/graph"
@@ -23,7 +22,7 @@ var (
 )
 
 func gnpUndirected(n int, p float64) graph.Undirected {
-	g := simple.NewUndirectedGraph(0, math.Inf(1))
+	g := simple.NewUndirectedGraph()
 	gen.Gnp(g, n, p, nil)
 	return g
 }
@@ -65,7 +64,7 @@ var (
 )
 
 func navigableSmallWorldUndirected(n, p, q int, r float64) graph.Undirected {
-	g := simple.NewUndirectedGraph(0, math.Inf(1))
+	g := simple.NewUndirectedGraph()
 	gen.NavigableSmallWorld(g, []int{n, n}, p, q, r, nil)
 	return g
 }
diff --git a/graph/path/dijkstra_test.go b/graph/path/dijkstra_test.go
index 0a71b9e7..ccb74644 100644
--- a/graph/path/dijkstra_test.go
+++ b/graph/path/dijkstra_test.go
@@ -19,7 +19,7 @@ func TestDijkstraFrom(t *testing.T) {
 	for _, test := range testgraphs.ShortestPathTests {
 		g := test.Graph()
 		for _, e := range test.Edges {
-			g.SetEdge(e)
+			g.SetWeightedEdge(e)
 		}
 
 		var (
@@ -85,7 +85,7 @@ func TestDijkstraAllPaths(t *testing.T) {
 	for _, test := range testgraphs.ShortestPathTests {
 		g := test.Graph()
 		for _, e := range test.Edges {
-			g.SetEdge(e)
+			g.SetWeightedEdge(e)
 		}
 
 		var (
diff --git a/graph/path/dynamic/dstarlite.go b/graph/path/dynamic/dstarlite.go
index bcbfdd79..0fd7904a 100644
--- a/graph/path/dynamic/dstarlite.go
+++ b/graph/path/dynamic/dstarlite.go
@@ -33,7 +33,7 @@ type DStarLite struct {
 // WorldModel is a mutable weighted directed graph that returns nodes identified
 // by id number.
 type WorldModel interface {
-	graph.Builder
+	graph.WeightedBuilder
 	graph.WeightedDirected
 	Node(id int64) graph.Node
 }
@@ -104,7 +104,7 @@ func NewDStarLite(s, t graph.Node, g graph.Graph, h path.Heuristic, m WorldModel
 			if w < 0 {
 				panic("D* Lite: negative edge weight")
 			}
-			d.model.SetEdge(simple.Edge{F: u, T: d.model.Node(v.ID()), W: w})
+			d.model.SetWeightedEdge(simple.Edge{F: u, T: d.model.Node(v.ID()), W: w})
 		}
 	}
 
@@ -302,7 +302,7 @@ func (d *DStarLite) UpdateWorld(changes []graph.Edge) {
 		cOld, _ := d.model.Weight(from, to)
 		u := d.worldNodeFor(from)
 		v := d.worldNodeFor(to)
-		d.model.SetEdge(simple.Edge{F: u, T: v, W: c})
+		d.model.SetWeightedEdge(simple.Edge{F: u, T: v, W: c})
 		if cOld > c {
 			if u.ID() != d.t.ID() {
 				u.rhs = math.Min(u.rhs, c+v.g)
diff --git a/graph/path/dynamic/dstarlite_test.go b/graph/path/dynamic/dstarlite_test.go
index 2733f5f6..bdfcc1a6 100644
--- a/graph/path/dynamic/dstarlite_test.go
+++ b/graph/path/dynamic/dstarlite_test.go
@@ -35,7 +35,7 @@ func TestDStarLiteNullHeuristic(t *testing.T) {
 
 		g := test.Graph()
 		for _, e := range test.Edges {
-			g.SetEdge(e)
+			g.SetWeightedEdge(e)
 		}
 
 		var (
@@ -47,7 +47,7 @@ func TestDStarLiteNullHeuristic(t *testing.T) {
 			defer func() {
 				panicked = recover() != nil
 			}()
-			d = NewDStarLite(test.Query.From(), test.Query.To(), g.(graph.Graph), path.NullHeuristic, simple.NewDirectedGraph(0, math.Inf(1)))
+			d = NewDStarLite(test.Query.From(), test.Query.To(), g.(graph.Graph), path.NullHeuristic, simple.NewWeightedDirectedGraph(0, math.Inf(1)))
 		}()
 		if panicked || test.HasNegativeWeight {
 			if !test.HasNegativeWeight {
@@ -579,7 +579,7 @@ func TestDStarLiteDynamic(t *testing.T) {
 				return test.heuristic(ax-bx, ay-by)
 			}
 
-			world := simple.NewDirectedGraph(0, math.Inf(1))
+			world := simple.NewWeightedDirectedGraph(0, math.Inf(1))
 			d := NewDStarLite(test.s, test.t, l, heuristic, world)
 			var (
 				dp  *dumper
diff --git a/graph/path/floydwarshall_test.go b/graph/path/floydwarshall_test.go
index 147658af..d23c0341 100644
--- a/graph/path/floydwarshall_test.go
+++ b/graph/path/floydwarshall_test.go
@@ -19,7 +19,7 @@ func TestFloydWarshall(t *testing.T) {
 	for _, test := range testgraphs.ShortestPathTests {
 		g := test.Graph()
 		for _, e := range test.Edges {
-			g.SetEdge(e)
+			g.SetWeightedEdge(e)
 		}
 
 		pt, ok := FloydWarshall(g.(graph.Graph))
diff --git a/graph/path/internal/testgraphs/shortest.go b/graph/path/internal/testgraphs/shortest.go
index 8d79f939..26a7e68c 100644
--- a/graph/path/internal/testgraphs/shortest.go
+++ b/graph/path/internal/testgraphs/shortest.go
@@ -25,7 +25,7 @@ func init() {
 // dynamic shortest path routine in path/dynamic: DStarLite.
 var ShortestPathTests = []struct {
 	Name              string
-	Graph             func() graph.EdgeAdder
+	Graph             func() graph.WeightedEdgeAdder
 	Edges             []simple.Edge
 	HasNegativeWeight bool
 	HasNegativeCycle  bool
@@ -40,7 +40,7 @@ var ShortestPathTests = []struct {
 	// Positive weighted graphs.
 	{
 		Name:  "empty directed",
-		Graph: func() graph.EdgeAdder { return simple.NewDirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
 
 		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(1)},
 		Weight: math.Inf(1),
@@ -49,7 +49,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "empty undirected",
-		Graph: func() graph.EdgeAdder { return simple.NewUndirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
 
 		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(1)},
 		Weight: math.Inf(1),
@@ -58,7 +58,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "one edge directed",
-		Graph: func() graph.EdgeAdder { return simple.NewDirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
 		Edges: []simple.Edge{
 			{F: simple.Node(0), T: simple.Node(1), W: 1},
 		},
@@ -74,7 +74,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "one edge self directed",
-		Graph: func() graph.EdgeAdder { return simple.NewDirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
 		Edges: []simple.Edge{
 			{F: simple.Node(0), T: simple.Node(1), W: 1},
 		},
@@ -90,7 +90,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "one edge undirected",
-		Graph: func() graph.EdgeAdder { return simple.NewUndirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
 		Edges: []simple.Edge{
 			{F: simple.Node(0), T: simple.Node(1), W: 1},
 		},
@@ -106,7 +106,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "two paths directed",
-		Graph: func() graph.EdgeAdder { return simple.NewDirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
 		Edges: []simple.Edge{
 			{F: simple.Node(0), T: simple.Node(2), W: 2},
 			{F: simple.Node(0), T: simple.Node(1), W: 1},
@@ -125,7 +125,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "two paths undirected",
-		Graph: func() graph.EdgeAdder { return simple.NewUndirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
 		Edges: []simple.Edge{
 			{F: simple.Node(0), T: simple.Node(2), W: 2},
 			{F: simple.Node(0), T: simple.Node(1), W: 1},
@@ -144,7 +144,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "confounding paths directed",
-		Graph: func() graph.EdgeAdder { return simple.NewDirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
 		Edges: []simple.Edge{
 			// Add a path from 0->5 of weight 4
 			{F: simple.Node(0), T: simple.Node(1), W: 1},
@@ -178,7 +178,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "confounding paths undirected",
-		Graph: func() graph.EdgeAdder { return simple.NewUndirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
 		Edges: []simple.Edge{
 			// Add a path from 0->5 of weight 4
 			{F: simple.Node(0), T: simple.Node(1), W: 1},
@@ -212,7 +212,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "confounding paths directed 2-step",
-		Graph: func() graph.EdgeAdder { return simple.NewDirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
 		Edges: []simple.Edge{
 			// Add a path from 0->5 of weight 4
 			{F: simple.Node(0), T: simple.Node(1), W: 1},
@@ -247,7 +247,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "confounding paths undirected 2-step",
-		Graph: func() graph.EdgeAdder { return simple.NewUndirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
 		Edges: []simple.Edge{
 			// Add a path from 0->5 of weight 4
 			{F: simple.Node(0), T: simple.Node(1), W: 1},
@@ -282,7 +282,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "zero-weight cycle directed",
-		Graph: func() graph.EdgeAdder { return simple.NewDirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
 		Edges: []simple.Edge{
 			// Add a path from 0->4 of weight 4
 			{F: simple.Node(0), T: simple.Node(1), W: 1},
@@ -306,7 +306,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "zero-weight cycle^2 directed",
-		Graph: func() graph.EdgeAdder { return simple.NewDirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
 		Edges: []simple.Edge{
 			// Add a path from 0->4 of weight 4
 			{F: simple.Node(0), T: simple.Node(1), W: 1},
@@ -333,7 +333,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "zero-weight cycle^2 confounding directed",
-		Graph: func() graph.EdgeAdder { return simple.NewDirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
 		Edges: []simple.Edge{
 			// Add a path from 0->4 of weight 4
 			{F: simple.Node(0), T: simple.Node(1), W: 1},
@@ -363,7 +363,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "zero-weight cycle^3 directed",
-		Graph: func() graph.EdgeAdder { return simple.NewDirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
 		Edges: []simple.Edge{
 			// Add a path from 0->4 of weight 4
 			{F: simple.Node(0), T: simple.Node(1), W: 1},
@@ -393,7 +393,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "zero-weight 3·cycle^2 confounding directed",
-		Graph: func() graph.EdgeAdder { return simple.NewDirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
 		Edges: []simple.Edge{
 			// Add a path from 0->4 of weight 4
 			{F: simple.Node(0), T: simple.Node(1), W: 1},
@@ -429,7 +429,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "zero-weight reversed 3·cycle^2 confounding directed",
-		Graph: func() graph.EdgeAdder { return simple.NewDirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
 		Edges: []simple.Edge{
 			// Add a path from 0->4 of weight 4
 			{F: simple.Node(0), T: simple.Node(1), W: 1},
@@ -465,7 +465,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "zero-weight |V|·cycle^(n/|V|) directed",
-		Graph: func() graph.EdgeAdder { return simple.NewDirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
 		Edges: func() []simple.Edge {
 			e := []simple.Edge{
 				// Add a path from 0->4 of weight 4
@@ -498,7 +498,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "zero-weight n·cycle directed",
-		Graph: func() graph.EdgeAdder { return simple.NewDirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
 		Edges: func() []simple.Edge {
 			e := []simple.Edge{
 				// Add a path from 0->4 of weight 4
@@ -531,7 +531,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "zero-weight bi-directional tree with single exit directed",
-		Graph: func() graph.EdgeAdder { return simple.NewDirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
 		Edges: func() []simple.Edge {
 			e := []simple.Edge{
 				// Add a path from 0->4 of weight 4
@@ -579,7 +579,7 @@ var ShortestPathTests = []struct {
 	// Negative weighted graphs.
 	{
 		Name:  "one edge directed negative",
-		Graph: func() graph.EdgeAdder { return simple.NewDirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
 		Edges: []simple.Edge{
 			{F: simple.Node(0), T: simple.Node(1), W: -1},
 		},
@@ -596,7 +596,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "one edge undirected negative",
-		Graph: func() graph.EdgeAdder { return simple.NewUndirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
 		Edges: []simple.Edge{
 			{F: simple.Node(0), T: simple.Node(1), W: -1},
 		},
@@ -607,7 +607,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "wp graph negative", // http://en.wikipedia.org/w/index.php?title=Johnson%27s_algorithm&oldid=564595231
-		Graph: func() graph.EdgeAdder { return simple.NewDirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
 		Edges: []simple.Edge{
 			{F: simple.Node('w'), T: simple.Node('z'), W: 2},
 			{F: simple.Node('x'), T: simple.Node('w'), W: 6},
@@ -630,7 +630,7 @@ var ShortestPathTests = []struct {
 	},
 	{
 		Name:  "roughgarden negative",
-		Graph: func() graph.EdgeAdder { return simple.NewDirectedGraph(0, math.Inf(1)) },
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
 		Edges: []simple.Edge{
 			{F: simple.Node('a'), T: simple.Node('b'), W: -2},
 			{F: simple.Node('b'), T: simple.Node('c'), W: -1},
diff --git a/graph/path/johnson_apsp_test.go b/graph/path/johnson_apsp_test.go
index 0d9d4500..1635ce92 100644
--- a/graph/path/johnson_apsp_test.go
+++ b/graph/path/johnson_apsp_test.go
@@ -19,7 +19,7 @@ func TestJohnsonAllPaths(t *testing.T) {
 	for _, test := range testgraphs.ShortestPathTests {
 		g := test.Graph()
 		for _, e := range test.Edges {
-			g.SetEdge(e)
+			g.SetWeightedEdge(e)
 		}
 
 		pt, ok := JohnsonAllPaths(g.(graph.Graph))
diff --git a/graph/path/spanning_tree_test.go b/graph/path/spanning_tree_test.go
index 8c7da7e5..f22d663b 100644
--- a/graph/path/spanning_tree_test.go
+++ b/graph/path/spanning_tree_test.go
@@ -26,7 +26,7 @@ func init() {
 }
 
 type spanningGraph interface {
-	graph.Builder
+	graph.WeightedBuilder
 	graph.WeightedUndirected
 	Edges() []graph.Edge
 }
@@ -40,7 +40,7 @@ var spanningTreeTests = []struct {
 }{
 	{
 		name:  "Empty",
-		graph: func() spanningGraph { return simple.NewUndirectedGraph(0, math.Inf(1)) },
+		graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
 		want:  0,
 	},
 	{
@@ -48,7 +48,7 @@ var spanningTreeTests = []struct {
 		// Modified to make edge weights unique; A--B is increased to 2.5 otherwise
 		// to prevent the alternative solution being found.
 		name:  "Prim WP figure 1",
-		graph: func() spanningGraph { return simple.NewUndirectedGraph(0, math.Inf(1)) },
+		graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
 		edges: []simple.Edge{
 			{F: simple.Node('A'), T: simple.Node('B'), W: 2.5},
 			{F: simple.Node('A'), T: simple.Node('D'), W: 1},
@@ -66,7 +66,7 @@ var spanningTreeTests = []struct {
 	{
 		// https://upload.wikimedia.org/wikipedia/commons/5/5c/MST_kruskal_en.gif
 		name:  "Kruskal WP figure 1",
-		graph: func() spanningGraph { return simple.NewUndirectedGraph(0, math.Inf(1)) },
+		graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
 		edges: []simple.Edge{
 			{F: simple.Node('a'), T: simple.Node('b'), W: 3},
 			{F: simple.Node('a'), T: simple.Node('e'), W: 1},
@@ -88,7 +88,7 @@ var spanningTreeTests = []struct {
 	{
 		// https://upload.wikimedia.org/wikipedia/commons/8/87/Kruskal_Algorithm_6.svg
 		name:  "Kruskal WP example",
-		graph: func() spanningGraph { return simple.NewUndirectedGraph(0, math.Inf(1)) },
+		graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
 		edges: []simple.Edge{
 			{F: simple.Node('A'), T: simple.Node('B'), W: 7},
 			{F: simple.Node('A'), T: simple.Node('D'), W: 5},
@@ -116,7 +116,7 @@ var spanningTreeTests = []struct {
 	{
 		// https://upload.wikimedia.org/wikipedia/commons/2/2e/Boruvka%27s_algorithm_%28Sollin%27s_algorithm%29_Anim.gif
 		name:  "Borůvka WP example",
-		graph: func() spanningGraph { return simple.NewUndirectedGraph(0, math.Inf(1)) },
+		graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
 		edges: []simple.Edge{
 			{F: simple.Node('A'), T: simple.Node('B'), W: 13},
 			{F: simple.Node('A'), T: simple.Node('C'), W: 6},
@@ -159,7 +159,7 @@ var spanningTreeTests = []struct {
 		// https://upload.wikimedia.org/wikipedia/commons/d/d2/Minimum_spanning_tree.svg
 		// Nodes labelled row major.
 		name:  "Minimum Spanning Tree WP figure 1",
-		graph: func() spanningGraph { return simple.NewUndirectedGraph(0, math.Inf(1)) },
+		graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
 		edges: []simple.Edge{
 			{F: simple.Node(1), T: simple.Node(2), W: 4},
 			{F: simple.Node(1), T: simple.Node(3), W: 1},
@@ -202,7 +202,7 @@ var spanningTreeTests = []struct {
 		// https://upload.wikimedia.org/wikipedia/commons/2/2e/Boruvka%27s_algorithm_%28Sollin%27s_algorithm%29_Anim.gif
 		// but with C--H and E--J cut.
 		name:  "Borůvka WP example cut",
-		graph: func() spanningGraph { return simple.NewUndirectedGraph(0, math.Inf(1)) },
+		graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
 		edges: []simple.Edge{
 			{F: simple.Node('A'), T: simple.Node('B'), W: 13},
 			{F: simple.Node('A'), T: simple.Node('C'), W: 6},
@@ -244,17 +244,17 @@ func testMinumumSpanning(mst func(dst graph.UndirectedBuilder, g spanningGraph)
 	for _, test := range spanningTreeTests {
 		g := test.graph()
 		for _, e := range test.edges {
-			g.SetEdge(e)
+			g.SetWeightedEdge(e)
 		}
 
-		dst := simple.NewUndirectedGraph(0, math.Inf(1))
+		dst := edgeAdder{simple.NewWeightedUndirectedGraph(0, math.Inf(1))}
 		w := mst(dst, g)
 		if w != test.want {
 			t.Errorf("unexpected minimum spanning tree weight for %q: got: %f want: %f",
 				test.name, w, test.want)
 		}
 		var got float64
-		for _, e := range dst.Edges() {
+		for _, e := range dst.WeightedEdges() {
 			got += e.Weight()
 		}
 		if got != test.want {
@@ -281,6 +281,18 @@ func testMinumumSpanning(mst func(dst graph.UndirectedBuilder, g spanningGraph)
 	}
 }
 
+type edgeAdder struct {
+	*simple.WeightedUndirectedGraph
+}
+
+func (g edgeAdder) NewEdge(x, y graph.Node) graph.Edge {
+	return g.WeightedUndirectedGraph.NewWeightedEdge(x, y, 1)
+}
+
+func (g edgeAdder) SetEdge(e graph.Edge) {
+	g.WeightedUndirectedGraph.SetWeightedEdge(e.(graph.WeightedEdge))
+}
+
 func TestKruskal(t *testing.T) {
 	testMinumumSpanning(func(dst graph.UndirectedBuilder, g spanningGraph) float64 {
 		return Kruskal(dst, g)
diff --git a/graph/simple/dense_directed_matrix.go b/graph/simple/dense_directed_matrix.go
index c9e61d6c..846c6f15 100644
--- a/graph/simple/dense_directed_matrix.go
+++ b/graph/simple/dense_directed_matrix.go
@@ -218,9 +218,19 @@ func (g *DirectedMatrix) Weight(x, y graph.Node) (w float64, ok bool) {
 	return g.absent, false
 }
 
-// SetEdge sets e, an edge from one node to another. If the ends of the edge are not in g
-// or the edge is a self loop, SetEdge panics.
+// SetEdge sets e, an edge from one node to another with unit weight. If the ends of the edge
+// are not in g or the edge is a self loop, SetEdge panics.
 func (g *DirectedMatrix) SetEdge(e graph.Edge) {
+	g.setWeightedEdge(e, 1)
+}
+
+// SetWeightedEdge sets e, an edge from one node to another. If the ends of the edge are not in g
+// or the edge is a self loop, SetWeightedEdge panics.
+func (g *DirectedMatrix) SetWeightedEdge(e graph.WeightedEdge) {
+	g.setWeightedEdge(e, e.Weight())
+}
+
+func (g *DirectedMatrix) setWeightedEdge(e graph.Edge, weight float64) {
 	fid := e.From().ID()
 	tid := e.To().ID()
 	if fid == tid {
@@ -233,7 +243,7 @@ func (g *DirectedMatrix) SetEdge(e graph.Edge) {
 		panic("simple: unavailable to node ID for dense graph")
 	}
 	// fid and tid are not greater than maximum int by this point.
-	g.mat.Set(int(fid), int(tid), e.Weight())
+	g.mat.Set(int(fid), int(tid), weight)
 }
 
 // RemoveEdge removes e from the graph, leaving the terminal nodes. If the edge does not exist
diff --git a/graph/simple/dense_undirected_matrix.go b/graph/simple/dense_undirected_matrix.go
index 117c0427..70672d6e 100644
--- a/graph/simple/dense_undirected_matrix.go
+++ b/graph/simple/dense_undirected_matrix.go
@@ -190,9 +190,19 @@ func (g *UndirectedMatrix) Weight(x, y graph.Node) (w float64, ok bool) {
 	return g.absent, false
 }
 
-// SetEdge sets e, an edge from one node to another. If the ends of the edge are not in g
-// or the edge is a self loop, SetEdge panics.
+// SetEdge sets e, an edge from one node to another with unit weight. If the ends of the edge are
+// not in g or the edge is a self loop, SetEdge panics.
 func (g *UndirectedMatrix) SetEdge(e graph.Edge) {
+	g.setWeightedEdge(e, 1)
+}
+
+// SetWeightedEdge sets e, an edge from one node to another. If the ends of the edge are not in g
+// or the edge is a self loop, SetWeightedEdge panics.
+func (g *UndirectedMatrix) SetWeightedEdge(e graph.WeightedEdge) {
+	g.setWeightedEdge(e, e.Weight())
+}
+
+func (g *UndirectedMatrix) setWeightedEdge(e graph.Edge, weight float64) {
 	fid := e.From().ID()
 	tid := e.To().ID()
 	if fid == tid {
@@ -205,7 +215,7 @@ func (g *UndirectedMatrix) SetEdge(e graph.Edge) {
 		panic("simple: unavailable to node ID for dense graph")
 	}
 	// fid and tid are not greater than maximum int by this point.
-	g.mat.SetSym(int(fid), int(tid), e.Weight())
+	g.mat.SetSym(int(fid), int(tid), weight)
 }
 
 // RemoveEdge removes e from the graph, leaving the terminal nodes. If the edge does not exist
diff --git a/graph/simple/directed.go b/graph/simple/directed.go
index 18483d2b..0796cb13 100644
--- a/graph/simple/directed.go
+++ b/graph/simple/directed.go
@@ -16,22 +16,17 @@ type DirectedGraph struct {
 	from  map[int64]map[int64]graph.Edge
 	to    map[int64]map[int64]graph.Edge
 
-	self, absent float64
-
 	nodeIDs idSet
 }
 
 // NewDirectedGraph returns a DirectedGraph with the specified self and absent
 // edge weight values.
-func NewDirectedGraph(self, absent float64) *DirectedGraph {
+func NewDirectedGraph() *DirectedGraph {
 	return &DirectedGraph{
 		nodes: make(map[int64]graph.Node),
 		from:  make(map[int64]map[int64]graph.Edge),
 		to:    make(map[int64]map[int64]graph.Edge),
 
-		self:   self,
-		absent: absent,
-
 		nodeIDs: newIDSet(),
 	}
 }
@@ -213,12 +208,6 @@ 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 {
-	return g.WeightedEdge(u, v)
-}
-
-// 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 *DirectedGraph) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
 	if _, ok := g.nodes[u.ID()]; !ok {
 		return nil
 	}
@@ -246,24 +235,6 @@ func (g *DirectedGraph) HasEdgeFromTo(u, v graph.Node) bool {
 	return true
 }
 
-// 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 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 *DirectedGraph) Weight(x, y graph.Node) (w float64, ok bool) {
-	xid := x.ID()
-	yid := y.ID()
-	if xid == yid {
-		return g.self, true
-	}
-	if to, ok := g.from[xid]; ok {
-		if e, ok := to[yid]; ok {
-			return e.Weight(), true
-		}
-	}
-	return g.absent, false
-}
-
 // 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 {
diff --git a/graph/simple/directed_test.go b/graph/simple/directed_test.go
index 488e90fb..b66845bd 100644
--- a/graph/simple/directed_test.go
+++ b/graph/simple/directed_test.go
@@ -5,7 +5,6 @@
 package simple
 
 import (
-	"math"
 	"testing"
 
 	"gonum.org/v1/gonum/graph"
@@ -14,9 +13,8 @@ import (
 var (
 	directedGraph = (*DirectedGraph)(nil)
 
-	_ graph.Graph            = directedGraph
-	_ graph.Directed         = directedGraph
-	_ graph.WeightedDirected = directedGraph
+	_ graph.Graph    = directedGraph
+	_ graph.Directed = directedGraph
 )
 
 // Tests Issue #27
@@ -36,10 +34,10 @@ func generateDummyGraph() *DirectedGraph {
 		{0, 2},
 	}
 
-	g := NewDirectedGraph(0, math.Inf(1))
+	g := NewDirectedGraph()
 
 	for _, n := range nodes {
-		g.SetEdge(Edge{F: Node(n.srcID), T: Node(n.targetID), W: 1})
+		g.SetEdge(Edge{F: Node(n.srcID), T: Node(n.targetID)})
 	}
 
 	return g
@@ -52,7 +50,7 @@ func TestIssue123DirectedGraph(t *testing.T) {
 			t.Errorf("unexpected panic: %v", r)
 		}
 	}()
-	g := NewDirectedGraph(0, math.Inf(1))
+	g := NewDirectedGraph()
 
 	n0 := g.NewNode()
 	g.AddNode(n0)
diff --git a/graph/simple/undirected.go b/graph/simple/undirected.go
index e3f1c214..7254e4a0 100644
--- a/graph/simple/undirected.go
+++ b/graph/simple/undirected.go
@@ -15,21 +15,16 @@ type UndirectedGraph struct {
 	nodes map[int64]graph.Node
 	edges map[int64]map[int64]graph.Edge
 
-	self, absent float64
-
 	nodeIDs idSet
 }
 
 // NewUndirectedGraph returns an UndirectedGraph with the specified self and absent
 // edge weight values.
-func NewUndirectedGraph(self, absent float64) *UndirectedGraph {
+func NewUndirectedGraph() *UndirectedGraph {
 	return &UndirectedGraph{
 		nodes: make(map[int64]graph.Node),
 		edges: make(map[int64]map[int64]graph.Edge),
 
-		self:   self,
-		absent: absent,
-
 		nodeIDs: newIDSet(),
 	}
 }
@@ -186,22 +181,11 @@ func (g *UndirectedGraph) 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 *UndirectedGraph) Edge(u, v graph.Node) graph.Edge {
-	return g.WeightedEdgeBetween(u, v)
-}
-
-// 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 *UndirectedGraph) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
-	return g.WeightedEdgeBetween(u, v)
+	return g.EdgeBetween(u, v)
 }
 
 // EdgeBetween returns the edge between nodes x and y.
 func (g *UndirectedGraph) EdgeBetween(x, y graph.Node) graph.Edge {
-	return g.WeightedEdgeBetween(x, y)
-}
-
-// WeightedEdgeBetween returns the weighted edge between nodes x and y.
-func (g *UndirectedGraph) WeightedEdgeBetween(x, y graph.Node) graph.WeightedEdge {
 	// We don't need to check if neigh exists because
 	// it's implicit in the edges access.
 	if !g.Has(x) {
@@ -211,24 +195,6 @@ func (g *UndirectedGraph) WeightedEdgeBetween(x, y graph.Node) graph.WeightedEdg
 	return g.edges[x.ID()][y.ID()]
 }
 
-// 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 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 *UndirectedGraph) Weight(x, y graph.Node) (w float64, ok bool) {
-	xid := x.ID()
-	yid := y.ID()
-	if xid == yid {
-		return g.self, true
-	}
-	if n, ok := g.edges[xid]; ok {
-		if e, ok := n[yid]; ok {
-			return e.Weight(), true
-		}
-	}
-	return g.absent, false
-}
-
 // Degree returns the degree of n in g.
 func (g *UndirectedGraph) Degree(n graph.Node) int {
 	if _, ok := g.nodes[n.ID()]; !ok {
diff --git a/graph/simple/undirected_test.go b/graph/simple/undirected_test.go
index 73b9f2e6..f5c0dafc 100644
--- a/graph/simple/undirected_test.go
+++ b/graph/simple/undirected_test.go
@@ -5,7 +5,6 @@
 package simple
 
 import (
-	"math"
 	"testing"
 
 	"gonum.org/v1/gonum/graph"
@@ -14,20 +13,19 @@ import (
 var (
 	undirectedGraph = (*UndirectedGraph)(nil)
 
-	_ graph.Graph              = undirectedGraph
-	_ graph.Undirected         = undirectedGraph
-	_ graph.WeightedUndirected = undirectedGraph
+	_ graph.Graph      = undirectedGraph
+	_ graph.Undirected = undirectedGraph
 )
 
 func TestAssertMutableNotDirected(t *testing.T) {
-	var g graph.UndirectedBuilder = NewUndirectedGraph(0, math.Inf(1))
+	var g graph.UndirectedBuilder = NewUndirectedGraph()
 	if _, ok := g.(graph.Directed); ok {
 		t.Fatal("Graph is directed, but a MutableGraph cannot safely be directed!")
 	}
 }
 
 func TestMaxID(t *testing.T) {
-	g := NewUndirectedGraph(0, math.Inf(1))
+	g := NewUndirectedGraph()
 	nodes := make(map[graph.Node]struct{})
 	for i := Node(0); i < 3; i++ {
 		g.AddNode(i)
@@ -54,7 +52,7 @@ func TestIssue123UndirectedGraph(t *testing.T) {
 			t.Errorf("unexpected panic: %v", r)
 		}
 	}()
-	g := NewUndirectedGraph(0, math.Inf(1))
+	g := NewUndirectedGraph()
 
 	n0 := g.NewNode()
 	g.AddNode(n0)
diff --git a/graph/simple/weighted_directed.go b/graph/simple/weighted_directed.go
new file mode 100644
index 00000000..00f8b475
--- /dev/null
+++ b/graph/simple/weighted_directed.go
@@ -0,0 +1,285 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package simple
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/graph"
+)
+
+// WeightedDirectedGraph implements a generalized weighted directed graph.
+type WeightedDirectedGraph struct {
+	nodes map[int64]graph.Node
+	from  map[int64]map[int64]graph.WeightedEdge
+	to    map[int64]map[int64]graph.WeightedEdge
+
+	self, absent float64
+
+	nodeIDs idSet
+}
+
+// NewWeightedDirectedGraph returns a WeightedDirectedGraph with the specified self and absent
+// edge weight values.
+func NewWeightedDirectedGraph(self, absent float64) *WeightedDirectedGraph {
+	return &WeightedDirectedGraph{
+		nodes: make(map[int64]graph.Node),
+		from:  make(map[int64]map[int64]graph.WeightedEdge),
+		to:    make(map[int64]map[int64]graph.WeightedEdge),
+
+		self:   self,
+		absent: absent,
+
+		nodeIDs: newIDSet(),
+	}
+}
+
+// NewNode returns a new unique Node to be added to g. The Node's ID does
+// not become valid in g until the Node is added to g.
+func (g *WeightedDirectedGraph) NewNode() graph.Node {
+	if len(g.nodes) == 0 {
+		return Node(0)
+	}
+	if int64(len(g.nodes)) == maxInt {
+		panic("simple: cannot allocate node: no slot")
+	}
+	return Node(g.nodeIDs.newID())
+}
+
+// AddNode adds n to the graph. It panics if the added node ID matches an existing node ID.
+func (g *WeightedDirectedGraph) AddNode(n graph.Node) {
+	if _, exists := g.nodes[n.ID()]; exists {
+		panic(fmt.Sprintf("simple: node ID collision: %d", n.ID()))
+	}
+	g.nodes[n.ID()] = n
+	g.from[n.ID()] = make(map[int64]graph.WeightedEdge)
+	g.to[n.ID()] = make(map[int64]graph.WeightedEdge)
+	g.nodeIDs.use(n.ID())
+}
+
+// RemoveNode removes n from the graph, as well as any edges attached to it. If the node
+// is not in the graph it is a no-op.
+func (g *WeightedDirectedGraph) RemoveNode(n graph.Node) {
+	if _, ok := g.nodes[n.ID()]; !ok {
+		return
+	}
+	delete(g.nodes, n.ID())
+
+	for from := range g.from[n.ID()] {
+		delete(g.to[from], n.ID())
+	}
+	delete(g.from, n.ID())
+
+	for to := range g.to[n.ID()] {
+		delete(g.from[to], n.ID())
+	}
+	delete(g.to, n.ID())
+
+	g.nodeIDs.release(n.ID())
+}
+
+// NewWeightedEdge returns a new weighted edge from the source to the destination node.
+func (g *WeightedDirectedGraph) NewWeightedEdge(from, to graph.Node, weight float64) graph.WeightedEdge {
+	return &Edge{F: from, T: to, W: weight}
+}
+
+// SetWeightedEdge adds a weighted edge from one node to another. If the nodes do not exist, they are added.
+// It will panic if the IDs of the e.From and e.To are equal.
+func (g *WeightedDirectedGraph) SetWeightedEdge(e graph.WeightedEdge) {
+	var (
+		from = e.From()
+		fid  = from.ID()
+		to   = e.To()
+		tid  = to.ID()
+	)
+
+	if fid == tid {
+		panic("simple: adding self edge")
+	}
+
+	if !g.Has(from) {
+		g.AddNode(from)
+	}
+	if !g.Has(to) {
+		g.AddNode(to)
+	}
+
+	g.from[fid][tid] = e
+	g.to[tid][fid] = e
+}
+
+// RemoveEdge removes e from the graph, leaving the terminal nodes. If the edge does not exist
+// it is a no-op.
+func (g *WeightedDirectedGraph) RemoveEdge(e graph.Edge) {
+	from, to := e.From(), e.To()
+	if _, ok := g.nodes[from.ID()]; !ok {
+		return
+	}
+	if _, ok := g.nodes[to.ID()]; !ok {
+		return
+	}
+
+	delete(g.from[from.ID()], to.ID())
+	delete(g.to[to.ID()], from.ID())
+}
+
+// Node returns the node in the graph with the given ID.
+func (g *WeightedDirectedGraph) Node(id int64) graph.Node {
+	return g.nodes[id]
+}
+
+// Has returns whether the node exists within the graph.
+func (g *WeightedDirectedGraph) Has(n graph.Node) bool {
+	_, ok := g.nodes[n.ID()]
+
+	return ok
+}
+
+// Nodes returns all the nodes in the graph.
+func (g *WeightedDirectedGraph) Nodes() []graph.Node {
+	nodes := make([]graph.Node, len(g.from))
+	i := 0
+	for _, n := range g.nodes {
+		nodes[i] = n
+		i++
+	}
+
+	return nodes
+}
+
+// Edges returns all the edges in the graph.
+func (g *WeightedDirectedGraph) Edges() []graph.Edge {
+	var edges []graph.Edge
+	for _, u := range g.nodes {
+		for _, e := range g.from[u.ID()] {
+			edges = append(edges, e)
+		}
+	}
+	return edges
+}
+
+// WeightedEdges returns all the weighted edges in the graph.
+func (g *WeightedDirectedGraph) WeightedEdges() []graph.WeightedEdge {
+	var edges []graph.WeightedEdge
+	for _, u := range g.nodes {
+		for _, e := range g.from[u.ID()] {
+			edges = append(edges, e)
+		}
+	}
+	return edges
+}
+
+// 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 {
+		return nil
+	}
+
+	from := make([]graph.Node, len(g.from[n.ID()]))
+	i := 0
+	for id := range g.from[n.ID()] {
+		from[i] = g.nodes[id]
+		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 {
+		return nil
+	}
+
+	to := make([]graph.Node, len(g.to[n.ID()]))
+	i := 0
+	for id := range g.to[n.ID()] {
+		to[i] = g.nodes[id]
+		i++
+	}
+
+	return to
+}
+
+// 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()
+	if _, ok := g.nodes[xid]; !ok {
+		return false
+	}
+	if _, ok := g.nodes[yid]; !ok {
+		return false
+	}
+	if _, ok := g.from[xid][yid]; ok {
+		return true
+	}
+	_, ok := g.from[yid][xid]
+	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 *WeightedDirectedGraph) Edge(u, v graph.Node) graph.Edge {
+	return g.WeightedEdge(u, v)
+}
+
+// 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 {
+	if _, ok := g.nodes[u.ID()]; !ok {
+		return nil
+	}
+	if _, ok := g.nodes[v.ID()]; !ok {
+		return nil
+	}
+	edge, ok := g.from[u.ID()][v.ID()]
+	if !ok {
+		return nil
+	}
+	return edge
+}
+
+// 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.nodes[u.ID()]; !ok {
+		return false
+	}
+	if _, ok := g.nodes[v.ID()]; !ok {
+		return false
+	}
+	if _, ok := g.from[u.ID()][v.ID()]; !ok {
+		return false
+	}
+	return true
+}
+
+// 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 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()
+	if xid == yid {
+		return g.self, true
+	}
+	if to, ok := g.from[xid]; ok {
+		if e, ok := to[yid]; ok {
+			return e.Weight(), true
+		}
+	}
+	return g.absent, false
+}
+
+// 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 {
+		return 0
+	}
+
+	return len(g.from[n.ID()]) + len(g.to[n.ID()])
+}
diff --git a/graph/simple/weighted_directed_test.go b/graph/simple/weighted_directed_test.go
new file mode 100644
index 00000000..12c929ee
--- /dev/null
+++ b/graph/simple/weighted_directed_test.go
@@ -0,0 +1,67 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package simple
+
+import (
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+)
+
+var (
+	weightedDirectedGraph = (*WeightedDirectedGraph)(nil)
+
+	_ graph.Graph            = weightedDirectedGraph
+	_ graph.Directed         = weightedDirectedGraph
+	_ graph.WeightedDirected = weightedDirectedGraph
+)
+
+// Tests Issue #27
+func TestWeightedEdgeOvercounting(t *testing.T) {
+	g := generateDummyGraph()
+
+	if neigh := g.From(Node(Node(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))
+	}
+}
+
+func generateDummyWeightedGraph() *WeightedDirectedGraph {
+	nodes := [4]struct{ srcID, targetID int }{
+		{2, 1},
+		{1, 0},
+		{2, 0},
+		{0, 2},
+	}
+
+	g := NewWeightedDirectedGraph(0, math.Inf(1))
+
+	for _, n := range nodes {
+		g.SetWeightedEdge(Edge{F: Node(n.srcID), T: Node(n.targetID), W: 1})
+	}
+
+	return g
+}
+
+// Test for issue #123 https://github.com/gonum/graph/issues/123
+func TestIssue123WeightedDirectedGraph(t *testing.T) {
+	defer func() {
+		if r := recover(); r != nil {
+			t.Errorf("unexpected panic: %v", r)
+		}
+	}()
+	g := NewWeightedDirectedGraph(0, math.Inf(1))
+
+	n0 := g.NewNode()
+	g.AddNode(n0)
+
+	n1 := g.NewNode()
+	g.AddNode(n1)
+
+	g.RemoveNode(n0)
+
+	n2 := g.NewNode()
+	g.AddNode(n2)
+}
diff --git a/graph/simple/weighted_undirected.go b/graph/simple/weighted_undirected.go
new file mode 100644
index 00000000..c8b67551
--- /dev/null
+++ b/graph/simple/weighted_undirected.go
@@ -0,0 +1,260 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package simple
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/graph"
+)
+
+// WeightedUndirectedGraph implements a generalized weighted undirected graph.
+type WeightedUndirectedGraph struct {
+	nodes map[int64]graph.Node
+	edges map[int64]map[int64]graph.WeightedEdge
+
+	self, absent float64
+
+	nodeIDs idSet
+}
+
+// NewWeightedUndirectedGraph returns an WeightedUndirectedGraph with the specified self and absent
+// edge weight values.
+func NewWeightedUndirectedGraph(self, absent float64) *WeightedUndirectedGraph {
+	return &WeightedUndirectedGraph{
+		nodes: make(map[int64]graph.Node),
+		edges: make(map[int64]map[int64]graph.WeightedEdge),
+
+		self:   self,
+		absent: absent,
+
+		nodeIDs: newIDSet(),
+	}
+}
+
+// NewNode returns a new unique Node to be added to g. The Node's ID does
+// not become valid in g until the Node is added to g.
+func (g *WeightedUndirectedGraph) NewNode() graph.Node {
+	if len(g.nodes) == 0 {
+		return Node(0)
+	}
+	if int64(len(g.nodes)) == maxInt {
+		panic("simple: cannot allocate node: no slot")
+	}
+	return Node(g.nodeIDs.newID())
+}
+
+// AddNode adds n to the graph. It panics if the added node ID matches an existing node ID.
+func (g *WeightedUndirectedGraph) AddNode(n graph.Node) {
+	if _, exists := g.nodes[n.ID()]; exists {
+		panic(fmt.Sprintf("simple: node ID collision: %d", n.ID()))
+	}
+	g.nodes[n.ID()] = n
+	g.edges[n.ID()] = make(map[int64]graph.WeightedEdge)
+	g.nodeIDs.use(n.ID())
+}
+
+// RemoveNode removes n from the graph, as well as any edges attached to it. If the node
+// is not in the graph it is a no-op.
+func (g *WeightedUndirectedGraph) RemoveNode(n graph.Node) {
+	if _, ok := g.nodes[n.ID()]; !ok {
+		return
+	}
+	delete(g.nodes, n.ID())
+
+	for from := range g.edges[n.ID()] {
+		delete(g.edges[from], n.ID())
+	}
+	delete(g.edges, n.ID())
+
+	g.nodeIDs.release(n.ID())
+}
+
+// NewWeightedEdge returns a new weighted edge from the source to the destination node.
+func (g *WeightedUndirectedGraph) NewWeightedEdge(from, to graph.Node, weight float64) graph.WeightedEdge {
+	return &Edge{F: from, T: to, W: weight}
+}
+
+// SetWeightedEdge adds a weighted edge from one node to another. If the nodes do not exist, they are added.
+// It will panic if the IDs of the e.From and e.To are equal.
+func (g *WeightedUndirectedGraph) SetWeightedEdge(e graph.WeightedEdge) {
+	var (
+		from = e.From()
+		fid  = from.ID()
+		to   = e.To()
+		tid  = to.ID()
+	)
+
+	if fid == tid {
+		panic("simple: adding self edge")
+	}
+
+	if !g.Has(from) {
+		g.AddNode(from)
+	}
+	if !g.Has(to) {
+		g.AddNode(to)
+	}
+
+	g.edges[fid][tid] = e
+	g.edges[tid][fid] = e
+}
+
+// RemoveEdge removes e from the graph, leaving the terminal nodes. If the edge does not exist
+// it is a no-op.
+func (g *WeightedUndirectedGraph) RemoveEdge(e graph.Edge) {
+	from, to := e.From(), e.To()
+	if _, ok := g.nodes[from.ID()]; !ok {
+		return
+	}
+	if _, ok := g.nodes[to.ID()]; !ok {
+		return
+	}
+
+	delete(g.edges[from.ID()], to.ID())
+	delete(g.edges[to.ID()], from.ID())
+}
+
+// Node returns the node in the graph with the given ID.
+func (g *WeightedUndirectedGraph) Node(id int64) graph.Node {
+	return g.nodes[id]
+}
+
+// Has returns whether the node exists within the graph.
+func (g *WeightedUndirectedGraph) Has(n graph.Node) bool {
+	_, ok := g.nodes[n.ID()]
+	return ok
+}
+
+// Nodes returns all the nodes in the graph.
+func (g *WeightedUndirectedGraph) Nodes() []graph.Node {
+	nodes := make([]graph.Node, len(g.nodes))
+	i := 0
+	for _, n := range g.nodes {
+		nodes[i] = n
+		i++
+	}
+
+	return nodes
+}
+
+// Edges returns all the edges in the graph.
+func (g *WeightedUndirectedGraph) Edges() []graph.Edge {
+	var edges []graph.Edge
+
+	seen := make(map[[2]int64]struct{})
+	for _, u := range g.edges {
+		for _, e := range u {
+			uid := e.From().ID()
+			vid := e.To().ID()
+			if _, ok := seen[[2]int64{uid, vid}]; ok {
+				continue
+			}
+			seen[[2]int64{uid, vid}] = struct{}{}
+			seen[[2]int64{vid, uid}] = struct{}{}
+			edges = append(edges, e)
+		}
+	}
+
+	return edges
+}
+
+// WeightedEdges returns all the weighted edges in the graph.
+func (g *WeightedUndirectedGraph) WeightedEdges() []graph.WeightedEdge {
+	var edges []graph.WeightedEdge
+
+	seen := make(map[[2]int64]struct{})
+	for _, u := range g.edges {
+		for _, e := range u {
+			uid := e.From().ID()
+			vid := e.To().ID()
+			if _, ok := seen[[2]int64{uid, vid}]; ok {
+				continue
+			}
+			seen[[2]int64{uid, vid}] = struct{}{}
+			seen[[2]int64{vid, uid}] = struct{}{}
+			edges = append(edges, e)
+		}
+	}
+
+	return edges
+}
+
+// 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) {
+		return nil
+	}
+
+	nodes := make([]graph.Node, len(g.edges[n.ID()]))
+	i := 0
+	for from := range g.edges[n.ID()] {
+		nodes[i] = g.nodes[from]
+		i++
+	}
+
+	return nodes
+}
+
+// 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()]
+	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)
+}
+
+// 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)
+}
+
+// EdgeBetween returns the edge between nodes x and y.
+func (g *WeightedUndirectedGraph) EdgeBetween(x, y graph.Node) graph.Edge {
+	return g.WeightedEdgeBetween(x, y)
+}
+
+// WeightedEdgeBetween returns the weighted edge between nodes x and y.
+func (g *WeightedUndirectedGraph) WeightedEdgeBetween(x, y graph.Node) graph.WeightedEdge {
+	// We don't need to check if neigh exists because
+	// it's implicit in the edges access.
+	if !g.Has(x) {
+		return nil
+	}
+
+	return g.edges[x.ID()][y.ID()]
+}
+
+// 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 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()
+	if xid == yid {
+		return g.self, true
+	}
+	if n, ok := g.edges[xid]; ok {
+		if e, ok := n[yid]; ok {
+			return e.Weight(), true
+		}
+	}
+	return g.absent, false
+}
+
+// Degree returns the degree of n in g.
+func (g *WeightedUndirectedGraph) Degree(n graph.Node) int {
+	if _, ok := g.nodes[n.ID()]; !ok {
+		return 0
+	}
+
+	return len(g.edges[n.ID()])
+}
diff --git a/graph/simple/weighted_undirected_test.go b/graph/simple/weighted_undirected_test.go
new file mode 100644
index 00000000..a3796ee3
--- /dev/null
+++ b/graph/simple/weighted_undirected_test.go
@@ -0,0 +1,69 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package simple
+
+import (
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+)
+
+var (
+	weightedUndirectedGraph = (*WeightedUndirectedGraph)(nil)
+
+	_ graph.Graph              = weightedUndirectedGraph
+	_ graph.Undirected         = weightedUndirectedGraph
+	_ graph.WeightedUndirected = weightedUndirectedGraph
+)
+
+func TestAssertWeightedMutableNotDirected(t *testing.T) {
+	var g graph.UndirectedWeightedBuilder = NewWeightedUndirectedGraph(0, math.Inf(1))
+	if _, ok := g.(graph.Directed); ok {
+		t.Fatal("Graph is directed, but a MutableGraph cannot safely be directed!")
+	}
+}
+
+func TestWeightedMaxID(t *testing.T) {
+	g := NewWeightedUndirectedGraph(0, math.Inf(1))
+	nodes := make(map[graph.Node]struct{})
+	for i := Node(0); i < 3; i++ {
+		g.AddNode(i)
+		nodes[i] = struct{}{}
+	}
+	g.RemoveNode(Node(0))
+	delete(nodes, Node(0))
+	g.RemoveNode(Node(2))
+	delete(nodes, Node(2))
+	n := g.NewNode()
+	g.AddNode(n)
+	if !g.Has(n) {
+		t.Error("added node does not exist in graph")
+	}
+	if _, exists := nodes[n]; exists {
+		t.Errorf("Created already existing node id: %v", n.ID())
+	}
+}
+
+// Test for issue #123 https://github.com/gonum/graph/issues/123
+func TestIssue123WeightedUndirectedGraph(t *testing.T) {
+	defer func() {
+		if r := recover(); r != nil {
+			t.Errorf("unexpected panic: %v", r)
+		}
+	}()
+	g := NewWeightedUndirectedGraph(0, math.Inf(1))
+
+	n0 := g.NewNode()
+	g.AddNode(n0)
+
+	n1 := g.NewNode()
+	g.AddNode(n1)
+
+	g.RemoveNode(n0)
+
+	n2 := g.NewNode()
+	g.AddNode(n2)
+}
diff --git a/graph/topo/bench_test.go b/graph/topo/bench_test.go
index fb23f46f..7b2bdc3e 100644
--- a/graph/topo/bench_test.go
+++ b/graph/topo/bench_test.go
@@ -5,7 +5,6 @@
 package topo
 
 import (
-	"math"
 	"testing"
 
 	"gonum.org/v1/gonum/graph"
@@ -23,7 +22,7 @@ var (
 )
 
 func gnpDirected(n int, p float64) graph.Directed {
-	g := simple.NewDirectedGraph(0, math.Inf(1))
+	g := simple.NewDirectedGraph()
 	gen.Gnp(g, n, p, nil)
 	return g
 }
diff --git a/graph/topo/bron_kerbosch_test.go b/graph/topo/bron_kerbosch_test.go
index 875c96e9..8fdb67c0 100644
--- a/graph/topo/bron_kerbosch_test.go
+++ b/graph/topo/bron_kerbosch_test.go
@@ -5,7 +5,6 @@
 package topo
 
 import (
-	"math"
 	"reflect"
 	"sort"
 	"testing"
@@ -51,7 +50,7 @@ var vOrderTests = []struct {
 
 func TestVertexOrdering(t *testing.T) {
 	for i, test := range vOrderTests {
-		g := simple.NewUndirectedGraph(0, math.Inf(1))
+		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
@@ -136,7 +135,7 @@ var bronKerboschTests = []struct {
 
 func TestBronKerbosch(t *testing.T) {
 	for i, test := range bronKerboschTests {
-		g := simple.NewUndirectedGraph(0, math.Inf(1))
+		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
diff --git a/graph/topo/johnson_cycles_test.go b/graph/topo/johnson_cycles_test.go
index 983a3834..bf53120d 100644
--- a/graph/topo/johnson_cycles_test.go
+++ b/graph/topo/johnson_cycles_test.go
@@ -5,7 +5,6 @@
 package topo
 
 import (
-	"math"
 	"reflect"
 	"sort"
 	"testing"
@@ -85,7 +84,7 @@ var cyclesInTests = []struct {
 
 func TestDirectedCyclesIn(t *testing.T) {
 	for i, test := range cyclesInTests {
-		g := simple.NewDirectedGraph(0, math.Inf(1))
+		g := simple.NewDirectedGraph()
 		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.
diff --git a/graph/topo/paton_cycles_test.go b/graph/topo/paton_cycles_test.go
index 556ae108..c36590be 100644
--- a/graph/topo/paton_cycles_test.go
+++ b/graph/topo/paton_cycles_test.go
@@ -5,7 +5,6 @@
 package topo
 
 import (
-	"math"
 	"reflect"
 	"sort"
 	"testing"
@@ -74,7 +73,7 @@ var undirectedCyclesInTests = []struct {
 
 func TestUndirectedCyclesIn(t *testing.T) {
 	for i, test := range undirectedCyclesInTests {
-		g := simple.NewUndirectedGraph(0, math.Inf(1))
+		g := simple.NewUndirectedGraph()
 		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.
diff --git a/graph/topo/tarjan_test.go b/graph/topo/tarjan_test.go
index 611103e7..8751c507 100644
--- a/graph/topo/tarjan_test.go
+++ b/graph/topo/tarjan_test.go
@@ -5,7 +5,6 @@
 package topo
 
 import (
-	"math"
 	"reflect"
 	"sort"
 	"testing"
@@ -130,7 +129,7 @@ var tarjanTests = []struct {
 
 func TestSort(t *testing.T) {
 	for i, test := range tarjanTests {
-		g := simple.NewDirectedGraph(0, math.Inf(1))
+		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
@@ -161,7 +160,7 @@ func TestSort(t *testing.T) {
 
 func TestTarjanSCC(t *testing.T) {
 	for i, test := range tarjanTests {
-		g := simple.NewDirectedGraph(0, math.Inf(1))
+		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
@@ -288,7 +287,7 @@ var stabilizedSortTests = []struct {
 
 func TestSortStabilized(t *testing.T) {
 	for i, test := range stabilizedSortTests {
-		g := simple.NewDirectedGraph(0, math.Inf(1))
+		g := simple.NewDirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
diff --git a/graph/topo/topo_test.go b/graph/topo/topo_test.go
index d0e66b25..bb75796d 100644
--- a/graph/topo/topo_test.go
+++ b/graph/topo/topo_test.go
@@ -5,7 +5,6 @@
 package topo
 
 import (
-	"math"
 	"reflect"
 	"sort"
 	"testing"
@@ -16,7 +15,7 @@ import (
 )
 
 func TestIsPath(t *testing.T) {
-	dg := simple.NewDirectedGraph(0, math.Inf(1))
+	dg := simple.NewDirectedGraph()
 	if !IsPathIn(dg, nil) {
 		t.Error("IsPath returns false on nil path")
 	}
@@ -33,7 +32,7 @@ func TestIsPath(t *testing.T) {
 	if IsPathIn(dg, p) {
 		t.Error("IsPath returns true on bad path of length 2")
 	}
-	dg.SetEdge(simple.Edge{F: p[0], T: p[1], W: 1})
+	dg.SetEdge(simple.Edge{F: p[0], T: p[1]})
 	if !IsPathIn(dg, p) {
 		t.Error("IsPath returns false on correct path of length 2")
 	}
@@ -42,13 +41,13 @@ func TestIsPath(t *testing.T) {
 		t.Error("IsPath erroneously returns true for a reverse path")
 	}
 	p = []graph.Node{p[1], p[0], simple.Node(2)}
-	dg.SetEdge(simple.Edge{F: p[1], T: p[2], W: 1})
+	dg.SetEdge(simple.Edge{F: p[1], T: p[2]})
 	if !IsPathIn(dg, p) {
 		t.Error("IsPath does not find a correct path for path > 2 nodes")
 	}
-	ug := simple.NewUndirectedGraph(0, math.Inf(1))
-	ug.SetEdge(simple.Edge{F: p[1], T: p[0], W: 1})
-	ug.SetEdge(simple.Edge{F: p[1], T: p[2], W: 1})
+	ug := simple.NewUndirectedGraph()
+	ug.SetEdge(simple.Edge{F: p[1], T: p[0]})
+	ug.SetEdge(simple.Edge{F: p[1], T: p[2]})
 	if !IsPathIn(dg, p) {
 		t.Error("IsPath does not correctly account for undirected behavior")
 	}
@@ -69,7 +68,7 @@ var pathExistsInUndirectedTests = []struct {
 
 func TestPathExistsInUndirected(t *testing.T) {
 	for i, test := range pathExistsInUndirectedTests {
-		g := simple.NewUndirectedGraph(0, math.Inf(1))
+		g := simple.NewUndirectedGraph()
 
 		for u, e := range test.g {
 			if !g.Has(simple.Node(u)) {
@@ -108,7 +107,7 @@ var pathExistsInDirectedTests = []struct {
 
 func TestPathExistsInDirected(t *testing.T) {
 	for i, test := range pathExistsInDirectedTests {
-		g := simple.NewDirectedGraph(0, math.Inf(1))
+		g := simple.NewDirectedGraph()
 
 		for u, e := range test.g {
 			if !g.Has(simple.Node(u)) {
@@ -145,7 +144,7 @@ var connectedComponentTests = []struct {
 
 func TestConnectedComponents(t *testing.T) {
 	for i, test := range connectedComponentTests {
-		g := simple.NewUndirectedGraph(0, math.Inf(1))
+		g := simple.NewUndirectedGraph()
 
 		for u, e := range test.g {
 			if !g.Has(simple.Node(u)) {
diff --git a/graph/traverse/traverse_test.go b/graph/traverse/traverse_test.go
index 8aec716d..ad817352 100644
--- a/graph/traverse/traverse_test.go
+++ b/graph/traverse/traverse_test.go
@@ -6,7 +6,6 @@ package traverse
 
 import (
 	"fmt"
-	"math"
 	"reflect"
 	"sort"
 	"testing"
@@ -134,7 +133,7 @@ var breadthFirstTests = []struct {
 
 func TestBreadthFirst(t *testing.T) {
 	for i, test := range breadthFirstTests {
-		g := simple.NewUndirectedGraph(0, math.Inf(1))
+		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
@@ -222,7 +221,7 @@ var depthFirstTests = []struct {
 
 func TestDepthFirst(t *testing.T) {
 	for i, test := range depthFirstTests {
-		g := simple.NewUndirectedGraph(0, math.Inf(1))
+		g := simple.NewUndirectedGraph()
 		for u, e := range test.g {
 			// Add nodes that are not defined by an edge.
 			if !g.Has(simple.Node(u)) {
@@ -283,7 +282,7 @@ var walkAllTests = []struct {
 
 func TestWalkAll(t *testing.T) {
 	for i, test := range walkAllTests {
-		g := simple.NewUndirectedGraph(0, math.Inf(1))
+		g := simple.NewUndirectedGraph()
 
 		for u, e := range test.g {
 			if !g.Has(simple.Node(u)) {
@@ -366,7 +365,7 @@ var (
 )
 
 func gnpUndirected(n int, p float64) graph.Undirected {
-	g := simple.NewUndirectedGraph(0, math.Inf(1))
+	g := simple.NewUndirectedGraph()
 	gen.Gnp(g, n, p, nil)
 	return g
 }
diff --git a/graph/undirect.go b/graph/undirect.go
index fdb4b27f..e045dad4 100644
--- a/graph/undirect.go
+++ b/graph/undirect.go
@@ -4,36 +4,12 @@
 
 package graph
 
-// Undirect converts a directed graph to an undirected graph, resolving
-// edge weight conflicts.
+// Undirect converts a directed graph to an undirected graph.
 type Undirect struct {
 	G Directed
-
-	// Absent is the value used to
-	// represent absent edge weights
-	// passed to Merge if the reverse
-	// edge is present.
-	Absent float64
-
-	// Merge defines how discordant edge
-	// weights in G are resolved. A merge
-	// is performed if at least one edge
-	// exists between the nodes being
-	// considered. The edges corresponding
-	// to the two weights are also passed,
-	// in the same order.
-	// The order of weight parameters
-	// passed to Merge is not defined, so
-	// the function should be commutative.
-	// If Merge is nil, the arithmetic
-	// mean is used to merge weights.
-	Merge func(x, y float64, xe, ye Edge) float64
 }
 
-var (
-	_ Undirected         = Undirect{}
-	_ WeightedUndirected = Undirect{}
-)
+var _ Undirected = Undirect{}
 
 // Has returns whether the node exists within the graph.
 func (g Undirect) Has(n Node) bool { return g.G.Has(n) }
@@ -68,51 +44,118 @@ func (g Undirect) HasEdgeBetween(x, y Node) bool { return g.G.HasEdgeBetween(x,
 // 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.WeightedEdgeBetween(u, v) }
-
-// 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 Undirect) WeightedEdge(u, v Node) WeightedEdge { return g.WeightedEdgeBetween(u, v) }
+func (g Undirect) Edge(u, v Node) Edge { return g.EdgeBetween(u, v) }
 
 // 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 {
-	return g.WeightedEdgeBetween(x, y)
-}
-
-// 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 Undirect) WeightedEdgeBetween(x, y Node) WeightedEdge {
 	fe := g.G.Edge(x, y)
 	re := g.G.Edge(y, x)
 	if fe == nil && re == nil {
 		return nil
 	}
 
-	var f, r float64
-	if wg, ok := g.G.(WeightedDirected); ok {
-		f, ok = wg.Weight(x, y)
-		if !ok {
-			f = g.Absent
+	return EdgePair{fe, re}
+}
+
+// UndirectWeighted converts a directed weighted graph to an undirected weighted graph,
+// resolving edge weight conflicts.
+type UndirectWeighted struct {
+	G WeightedDirected
+
+	// Absent is the value used to
+	// represent absent edge weights
+	// passed to Merge if the reverse
+	// edge is present.
+	Absent float64
+
+	// Merge defines how discordant edge
+	// weights in G are resolved. A merge
+	// is performed if at least one edge
+	// exists between the nodes being
+	// considered. The edges corresponding
+	// to the two weights are also passed,
+	// in the same order.
+	// The order of weight parameters
+	// passed to Merge is not defined, so
+	// the function should be commutative.
+	// If Merge is nil, the arithmetic
+	// mean is used to merge weights.
+	Merge func(x, y float64, xe, ye Edge) float64
+}
+
+var (
+	_ Undirected         = UndirectWeighted{}
+	_ WeightedUndirected = UndirectWeighted{}
+)
+
+// Has returns whether the node exists within the graph.
+func (g UndirectWeighted) Has(n Node) bool { return g.G.Has(n) }
+
+// 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 {
+	var nodes []Node
+	seen := make(map[int64]struct{})
+	for _, n := range g.G.From(u) {
+		seen[n.ID()] = struct{}{}
+		nodes = append(nodes, n)
+	}
+	for _, n := range g.G.To(u) {
+		id := n.ID()
+		if _, ok := seen[id]; ok {
+			continue
 		}
-		r, ok = wg.Weight(y, x)
-		if !ok {
-			r = g.Absent
-		}
-	} else {
+		seen[n.ID()] = struct{}{}
+		nodes = append(nodes, n)
+	}
+	return nodes
+}
+
+// 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) }
+
+// 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) }
+
+// 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) }
+
+// 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)
+}
+
+// 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)
+	if fe == nil && re == nil {
+		return nil
+	}
+
+	f, ok := g.G.Weight(x, y)
+	if !ok {
 		f = g.Absent
-		if fe != nil {
-			f = fe.Weight()
-		}
+	}
+	r, ok := g.G.Weight(y, x)
+	if !ok {
 		r = g.Absent
-		if re != nil {
-			r = re.Weight()
-		}
 	}
 
 	var w float64
@@ -121,41 +164,26 @@ func (g Undirect) WeightedEdgeBetween(x, y Node) WeightedEdge {
 	} else {
 		w = g.Merge(f, r, fe, re)
 	}
-	return EdgePair{E: [2]Edge{fe, re}, W: w}
+	return WeightedEdgePair{EdgePair: [2]Edge{fe, re}, W: 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 Undirect) Weight(x, y Node) (w float64, ok bool) {
+func (g UndirectWeighted) Weight(x, y Node) (w float64, ok bool) {
 	fe := g.G.Edge(x, y)
 	re := g.G.Edge(y, x)
 
-	var f, r float64
-	if wg, wOk := g.G.(WeightedDirected); wOk {
-		var fOk, rOK bool
-		f, fOk = wg.Weight(x, y)
-		if !fOk {
-			f = g.Absent
-		}
-		r, rOK = wg.Weight(y, x)
-		if !rOK {
-			r = g.Absent
-		}
-		ok = fOk || rOK
-	} else {
+	f, fOk := g.G.Weight(x, y)
+	if !fOk {
 		f = g.Absent
-		if fe != nil {
-			f = fe.Weight()
-			ok = true
-		}
-		r = g.Absent
-		if re != nil {
-			r = re.Weight()
-			ok = true
-		}
 	}
+	r, rOK := g.G.Weight(y, x)
+	if !rOK {
+		r = g.Absent
+	}
+	ok = fOk || rOK
 
 	if g.Merge == nil {
 		return (f + r) / 2, ok
@@ -164,30 +192,33 @@ func (g Undirect) Weight(x, y Node) (w float64, ok bool) {
 }
 
 // EdgePair is an opposed pair of directed edges.
-type EdgePair struct {
-	E [2]Edge
-	W float64
-}
+type EdgePair [2]Edge
 
 // From returns the from node of the first non-nil edge, or nil.
 func (e EdgePair) From() Node {
-	if e.E[0] != nil {
-		return e.E[0].From()
-	} else if e.E[1] != nil {
-		return e.E[1].From()
+	if e[0] != nil {
+		return e[0].From()
+	} else if e[1] != nil {
+		return e[1].From()
 	}
 	return nil
 }
 
 // To returns the to node of the first non-nil edge, or nil.
 func (e EdgePair) To() Node {
-	if e.E[0] != nil {
-		return e.E[0].To()
-	} else if e.E[1] != nil {
-		return e.E[1].To()
+	if e[0] != nil {
+		return e[0].To()
+	} else if e[1] != nil {
+		return e[1].To()
 	}
 	return nil
 }
 
+// WeightedEdgePair is an opposed pair of directed edges.
+type WeightedEdgePair struct {
+	EdgePair
+	W float64
+}
+
 // Weight returns the merged edge weights of the two edges.
-func (e EdgePair) Weight() float64 { return e.W }
+func (e WeightedEdgePair) Weight() float64 { return e.W }
diff --git a/graph/undirect_test.go b/graph/undirect_test.go
index f5530608..d9ed6a05 100644
--- a/graph/undirect_test.go
+++ b/graph/undirect_test.go
@@ -13,8 +13,15 @@ import (
 	"gonum.org/v1/gonum/mat"
 )
 
-var directedGraphs = []struct {
-	g      func() graph.DirectedBuilder
+type weightedDirectedBuilder interface {
+	graph.WeightedBuilder
+	graph.WeightedDirected
+}
+
+var weightedDirectedGraphs = []struct {
+	skipUnweighted bool
+
+	g      func() weightedDirectedBuilder
 	edges  []simple.Edge
 	absent float64
 	merge  func(x, y float64, xe, ye graph.Edge) float64
@@ -22,7 +29,7 @@ var directedGraphs = []struct {
 	want mat.Matrix
 }{
 	{
-		g: func() graph.DirectedBuilder { return simple.NewDirectedGraph(0, 0) },
+		g: func() weightedDirectedBuilder { return simple.NewWeightedDirectedGraph(0, 0) },
 		edges: []simple.Edge{
 			{F: simple.Node(0), T: simple.Node(1), W: 2},
 			{F: simple.Node(1), T: simple.Node(0), W: 1},
@@ -35,7 +42,7 @@ var directedGraphs = []struct {
 		}),
 	},
 	{
-		g: func() graph.DirectedBuilder { return simple.NewDirectedGraph(0, 0) },
+		g: func() weightedDirectedBuilder { return simple.NewWeightedDirectedGraph(0, 0) },
 		edges: []simple.Edge{
 			{F: simple.Node(0), T: simple.Node(1), W: 2},
 			{F: simple.Node(1), T: simple.Node(0), W: 1},
@@ -50,7 +57,9 @@ var directedGraphs = []struct {
 		}),
 	},
 	{
-		g: func() graph.DirectedBuilder { return simple.NewDirectedGraph(0, 0) },
+		skipUnweighted: true, // The min merge function cannot be used in the unweighted case.
+
+		g: func() weightedDirectedBuilder { return simple.NewWeightedDirectedGraph(0, 0) },
 		edges: []simple.Edge{
 			{F: simple.Node(0), T: simple.Node(1), W: 2},
 			{F: simple.Node(1), T: simple.Node(0), W: 1},
@@ -64,7 +73,7 @@ var directedGraphs = []struct {
 		}),
 	},
 	{
-		g: func() graph.DirectedBuilder { return simple.NewDirectedGraph(0, 0) },
+		g: func() weightedDirectedBuilder { return simple.NewWeightedDirectedGraph(0, 0) },
 		edges: []simple.Edge{
 			{F: simple.Node(0), T: simple.Node(1), W: 2},
 			{F: simple.Node(1), T: simple.Node(0), W: 1},
@@ -86,7 +95,7 @@ var directedGraphs = []struct {
 		}),
 	},
 	{
-		g: func() graph.DirectedBuilder { return simple.NewDirectedGraph(0, 0) },
+		g: func() weightedDirectedBuilder { return simple.NewWeightedDirectedGraph(0, 0) },
 		edges: []simple.Edge{
 			{F: simple.Node(0), T: simple.Node(1), W: 2},
 			{F: simple.Node(1), T: simple.Node(0), W: 1},
@@ -102,13 +111,16 @@ var directedGraphs = []struct {
 }
 
 func TestUndirect(t *testing.T) {
-	for _, test := range directedGraphs {
+	for i, test := range weightedDirectedGraphs {
+		if test.skipUnweighted {
+			continue
+		}
 		g := test.g()
 		for _, e := range test.edges {
-			g.SetEdge(e)
+			g.SetWeightedEdge(e)
 		}
 
-		src := graph.Undirect{G: g, Absent: test.absent, Merge: test.merge}
+		src := graph.Undirect{G: g}
 		dst := simple.NewUndirectedMatrixFrom(src.Nodes(), 0, 0, 0)
 		for _, u := range src.Nodes() {
 			for _, v := range src.From(u) {
@@ -116,11 +128,48 @@ func TestUndirect(t *testing.T) {
 			}
 		}
 
+		want := unit{test.want}
+		if !mat.Equal(dst.Matrix(), want) {
+			t.Errorf("unexpected result for case %d:\ngot:\n%.4v\nwant:\n%.4v", i,
+				mat.Formatted(dst.Matrix()),
+				mat.Formatted(want),
+			)
+		}
+	}
+}
+
+func TestUndirectWeighted(t *testing.T) {
+	for i, test := range weightedDirectedGraphs {
+		g := test.g()
+		for _, e := range test.edges {
+			g.SetWeightedEdge(e)
+		}
+
+		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))
+			}
+		}
+
 		if !mat.Equal(dst.Matrix(), test.want) {
-			t.Errorf("unexpected result:\ngot:\n%.4v\nwant:\n%.4v",
+			t.Errorf("unexpected result for case %d:\ngot:\n%.4v\nwant:\n%.4v", i,
 				mat.Formatted(dst.Matrix()),
 				mat.Formatted(test.want),
 			)
 		}
 	}
 }
+
+type unit struct {
+	mat.Matrix
+}
+
+func (m unit) At(i, j int) float64 {
+	v := m.Matrix.At(i, j)
+	if v == 0 {
+		return 0
+	}
+	return 1
+}