graph: add Empty universal iterator for empty returns

graph/doc.go

@@ -3,4 +3,7 @@
 // license that can be found in the LICENSE file.
 
 // Package graph defines graph interfaces.
+//
+// Routines to test contract compliance by user implemented graph types
+// are available in gonum.org/v1/gonum/graph/testgraph.
 package graph // import "gonum.org/v1/gonum/graph"

graph/graph.go

@@ -32,10 +32,14 @@ type Graph interface {
 	Node(id int64) Node
 
 	// Nodes returns all the nodes in the graph.
+	//
+	// Nodes must not return nil.
 	Nodes() Nodes
 
 	// From returns all nodes that can be reached directly
 	// from the node with the given ID.
+	//
+	// From must not return nil.
 	From(id int64) Nodes
 
 	// HasEdgeBetween returns whether an edge exists between
@@ -99,6 +103,8 @@ type Directed interface {
 
 	// To returns all nodes that can reach directly
 	// to the node with the given ID.
+	//
+	// To must not return nil.
 	To(id int64) Nodes
 }
 
@@ -113,6 +119,8 @@ type WeightedDirected interface {
 
 	// To returns all nodes that can reach directly
 	// to the node with the given ID.
+	//
+	// To must not return nil.
 	To(id int64) Nodes
 }
 

graph/multi/directed.go

@@ -73,7 +73,7 @@ func (g *DirectedGraph) Edge(uid, vid int64) graph.Edge {
 // is a multi.Edge.
 func (g *DirectedGraph) Edges() graph.Edges {
 	if len(g.nodes) == 0 {
-		return nil
+		return graph.Empty
 	}
 	var edges []graph.Edge
 	for _, u := range g.nodes {
@@ -91,13 +91,16 @@ func (g *DirectedGraph) Edges() graph.Edges {
 			}
 		}
 	}
+	if len(edges) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedEdges(edges)
 }
 
 // From returns all nodes in g that can be reached directly from n.
 func (g *DirectedGraph) From(id int64) graph.Nodes {
 	if _, ok := g.from[id]; !ok {
-		return nil
+		return graph.Empty
 	}
 
 	from := make([]graph.Node, len(g.from[id]))
@@ -106,6 +109,9 @@ func (g *DirectedGraph) From(id int64) graph.Nodes {
 		from[i] = g.nodes[vid]
 		i++
 	}
+	if len(from) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedNodes(from)
 }
 
@@ -130,7 +136,7 @@ func (g *DirectedGraph) HasEdgeFromTo(uid, vid int64) bool {
 func (g *DirectedGraph) Lines(uid, vid int64) graph.Lines {
 	edge := g.from[uid][vid]
 	if len(edge) == 0 {
-		return nil
+		return graph.Empty
 	}
 	var lines []graph.Line
 	for _, l := range edge {
@@ -167,7 +173,7 @@ func (g *DirectedGraph) Node(id int64) graph.Node {
 // Nodes returns all the nodes in the graph.
 func (g *DirectedGraph) Nodes() graph.Nodes {
 	if len(g.nodes) == 0 {
-		return nil
+		return graph.Empty
 	}
 	nodes := make([]graph.Node, len(g.nodes))
 	i := 0
@@ -256,7 +262,7 @@ func (g *DirectedGraph) SetLine(l graph.Line) {
 // To returns all nodes in g that can reach directly to n.
 func (g *DirectedGraph) To(id int64) graph.Nodes {
 	if _, ok := g.from[id]; !ok {
-		return nil
+		return graph.Empty
 	}
 
 	to := make([]graph.Node, len(g.to[id]))
@@ -265,5 +271,8 @@ func (g *DirectedGraph) To(id int64) graph.Nodes {
 		to[i] = g.nodes[uid]
 		i++
 	}
+	if len(to) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedNodes(to)
 }

graph/multi/directed_test.go

@@ -53,16 +53,16 @@ func TestDirected(t *testing.T) {
 		testgraph.NodeExistence(t, directedBuilder)
 	})
 	t.Run("ReturnAdjacentNodes", func(t *testing.T) {
-		testgraph.ReturnAdjacentNodes(t, directedBuilder)
+		testgraph.ReturnAdjacentNodes(t, directedBuilder, true)
 	})
 	t.Run("ReturnAllLines", func(t *testing.T) {
-		testgraph.ReturnAllLines(t, directedBuilder)
+		testgraph.ReturnAllLines(t, directedBuilder, true)
 	})
 	t.Run("ReturnAllNodes", func(t *testing.T) {
-		testgraph.ReturnAllNodes(t, directedBuilder)
+		testgraph.ReturnAllNodes(t, directedBuilder, true)
 	})
 	t.Run("ReturnNodeSlice", func(t *testing.T) {
-		testgraph.ReturnNodeSlice(t, directedBuilder)
+		testgraph.ReturnNodeSlice(t, directedBuilder, true)
 	})
 }
 

graph/multi/doc.go

@@ -4,4 +4,6 @@
 
 // Package multi provides a suite of multigraph implementations satisfying
 // the gonum/graph interfaces.
+//
+// All types in multi return the graph.Empty value for empty iterators.
 package multi // import "gonum.org/v1/gonum/graph/multi"

graph/multi/undirected.go

@@ -75,7 +75,7 @@ func (g *UndirectedGraph) EdgeBetween(xid, yid int64) graph.Edge {
 // is a multi.Edge.
 func (g *UndirectedGraph) Edges() graph.Edges {
 	if len(g.lines) == 0 {
-		return nil
+		return graph.Empty
 	}
 	var edges []graph.Edge
 	seen := make(map[int64]struct{})
@@ -99,13 +99,16 @@ func (g *UndirectedGraph) Edges() graph.Edges {
 			}
 		}
 	}
+	if len(edges) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedEdges(edges)
 }
 
 // From returns all nodes in g that can be reached directly from n.
 func (g *UndirectedGraph) From(id int64) graph.Nodes {
 	if _, ok := g.nodes[id]; !ok {
-		return nil
+		return graph.Empty
 	}
 
 	nodes := make([]graph.Node, len(g.lines[id]))
@@ -114,6 +117,9 @@ func (g *UndirectedGraph) From(id int64) graph.Nodes {
 		nodes[i] = g.nodes[from]
 		i++
 	}
+	if len(nodes) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedNodes(nodes)
 }
 
@@ -132,7 +138,7 @@ func (g *UndirectedGraph) Lines(uid, vid int64) graph.Lines {
 // LinesBetween returns the lines between nodes x and y.
 func (g *UndirectedGraph) LinesBetween(xid, yid int64) graph.Lines {
 	if !g.HasEdgeBetween(xid, yid) {
-		return nil
+		return graph.Empty
 	}
 	var lines []graph.Line
 	for _, l := range g.lines[xid][yid] {
@@ -169,7 +175,7 @@ func (g *UndirectedGraph) Node(id int64) graph.Node {
 // Nodes returns all the nodes in the graph.
 func (g *UndirectedGraph) Nodes() graph.Nodes {
 	if len(g.nodes) == 0 {
-		return nil
+		return graph.Empty
 	}
 	nodes := make([]graph.Node, len(g.nodes))
 	i := 0

graph/multi/undirected_test.go

@@ -53,16 +53,16 @@ func TestUndirected(t *testing.T) {
 		testgraph.NodeExistence(t, undirectedBuilder)
 	})
 	t.Run("ReturnAdjacentNodes", func(t *testing.T) {
-		testgraph.ReturnAdjacentNodes(t, undirectedBuilder)
+		testgraph.ReturnAdjacentNodes(t, undirectedBuilder, true)
 	})
 	t.Run("ReturnAllLines", func(t *testing.T) {
-		testgraph.ReturnAllLines(t, undirectedBuilder)
+		testgraph.ReturnAllLines(t, undirectedBuilder, true)
 	})
 	t.Run("ReturnAllNodes", func(t *testing.T) {
-		testgraph.ReturnAllNodes(t, undirectedBuilder)
+		testgraph.ReturnAllNodes(t, undirectedBuilder, true)
 	})
 	t.Run("ReturnNodeSlice", func(t *testing.T) {
-		testgraph.ReturnNodeSlice(t, undirectedBuilder)
+		testgraph.ReturnNodeSlice(t, undirectedBuilder, true)
 	})
 }
 

graph/multi/weighted_directed.go

@@ -78,7 +78,7 @@ func (g *WeightedDirectedGraph) Edge(uid, vid int64) graph.Edge {
 // is a multi.WeightedEdge.
 func (g *WeightedDirectedGraph) Edges() graph.Edges {
 	if len(g.nodes) == 0 {
-		return nil
+		return graph.Empty
 	}
 	var edges []graph.Edge
 	for _, u := range g.nodes {
@@ -97,13 +97,16 @@ func (g *WeightedDirectedGraph) Edges() graph.Edges {
 			}
 		}
 	}
+	if len(edges) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedEdges(edges)
 }
 
 // From returns all nodes in g that can be reached directly from n.
 func (g *WeightedDirectedGraph) From(id int64) graph.Nodes {
 	if _, ok := g.from[id]; !ok {
-		return nil
+		return graph.Empty
 	}
 
 	from := make([]graph.Node, len(g.from[id]))
@@ -112,6 +115,9 @@ func (g *WeightedDirectedGraph) From(id int64) graph.Nodes {
 		from[i] = g.nodes[vid]
 		i++
 	}
+	if len(from) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedNodes(from)
 }
 
@@ -138,7 +144,7 @@ func (g *WeightedDirectedGraph) HasEdgeFromTo(uid, vid int64) bool {
 func (g *WeightedDirectedGraph) Lines(uid, vid int64) graph.Lines {
 	edge := g.from[uid][vid]
 	if len(edge) == 0 {
-		return nil
+		return graph.Empty
 	}
 	var lines []graph.Line
 	for _, l := range edge {
@@ -175,7 +181,7 @@ func (g *WeightedDirectedGraph) Node(id int64) graph.Node {
 // Nodes returns all the nodes in the graph.
 func (g *WeightedDirectedGraph) Nodes() graph.Nodes {
 	if len(g.nodes) == 0 {
-		return nil
+		return graph.Empty
 	}
 	nodes := make([]graph.Node, len(g.nodes))
 	i := 0
@@ -265,7 +271,7 @@ func (g *WeightedDirectedGraph) SetWeightedLine(l graph.WeightedLine) {
 // To returns all nodes in g that can reach directly to n.
 func (g *WeightedDirectedGraph) To(id int64) graph.Nodes {
 	if _, ok := g.from[id]; !ok {
-		return nil
+		return graph.Empty
 	}
 
 	to := make([]graph.Node, len(g.to[id]))
@@ -274,6 +280,9 @@ func (g *WeightedDirectedGraph) To(id int64) graph.Nodes {
 		to[i] = g.nodes[uid]
 		i++
 	}
+	if len(to) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedNodes(to)
 }
 
@@ -303,7 +312,7 @@ func (g *WeightedDirectedGraph) WeightedEdge(uid, vid int64) graph.WeightedEdge
 // is a multi.WeightedEdge.
 func (g *WeightedDirectedGraph) WeightedEdges() graph.WeightedEdges {
 	if len(g.nodes) == 0 {
-		return nil
+		return graph.Empty
 	}
 	var edges []graph.WeightedEdge
 	for _, u := range g.nodes {
@@ -322,6 +331,9 @@ func (g *WeightedDirectedGraph) WeightedEdges() graph.WeightedEdges {
 			}
 		}
 	}
+	if len(edges) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedWeightedEdges(edges)
 }
 
@@ -330,7 +342,7 @@ func (g *WeightedDirectedGraph) WeightedEdges() graph.WeightedEdges {
 func (g *WeightedDirectedGraph) WeightedLines(uid, vid int64) graph.WeightedLines {
 	edge := g.from[uid][vid]
 	if len(edge) == 0 {
-		return nil
+		return graph.Empty
 	}
 	var lines []graph.WeightedLine
 	for _, l := range edge {

graph/multi/weighted_directed_test.go

@@ -65,19 +65,19 @@ func TestWeightedDirected(t *testing.T) {
 		testgraph.NodeExistence(t, weightedDirectedBuilder)
 	})
 	t.Run("ReturnAdjacentNodes", func(t *testing.T) {
-		testgraph.ReturnAdjacentNodes(t, weightedDirectedBuilder)
+		testgraph.ReturnAdjacentNodes(t, weightedDirectedBuilder, true)
 	})
 	t.Run("ReturnAllLines", func(t *testing.T) {
-		testgraph.ReturnAllLines(t, weightedDirectedBuilder)
+		testgraph.ReturnAllLines(t, weightedDirectedBuilder, true)
 	})
 	t.Run("ReturnAllNodes", func(t *testing.T) {
-		testgraph.ReturnAllNodes(t, weightedDirectedBuilder)
+		testgraph.ReturnAllNodes(t, weightedDirectedBuilder, true)
 	})
 	t.Run("ReturnAllWeightedLines", func(t *testing.T) {
-		testgraph.ReturnAllWeightedLines(t, weightedDirectedBuilder)
+		testgraph.ReturnAllWeightedLines(t, weightedDirectedBuilder, true)
 	})
 	t.Run("ReturnNodeSlice", func(t *testing.T) {
-		testgraph.ReturnNodeSlice(t, weightedDirectedBuilder)
+		testgraph.ReturnNodeSlice(t, weightedDirectedBuilder, true)
 	})
 	t.Run("Weight", func(t *testing.T) {
 		testgraph.Weight(t, weightedDirectedBuilder)

graph/multi/weighted_undirected.go

@@ -80,7 +80,7 @@ func (g *WeightedUndirectedGraph) EdgeBetween(xid, yid int64) graph.Edge {
 // is a multi.Edge.
 func (g *WeightedUndirectedGraph) Edges() graph.Edges {
 	if len(g.lines) == 0 {
-		return nil
+		return graph.Empty
 	}
 	var edges []graph.Edge
 	seen := make(map[int64]struct{})
@@ -105,13 +105,16 @@ func (g *WeightedUndirectedGraph) Edges() graph.Edges {
 			}
 		}
 	}
+	if len(edges) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedEdges(edges)
 }
 
 // From returns all nodes in g that can be reached directly from n.
 func (g *WeightedUndirectedGraph) From(id int64) graph.Nodes {
 	if _, ok := g.nodes[id]; !ok {
-		return nil
+		return graph.Empty
 	}
 
 	nodes := make([]graph.Node, len(g.lines[id]))
@@ -120,6 +123,9 @@ func (g *WeightedUndirectedGraph) From(id int64) graph.Nodes {
 		nodes[i] = g.nodes[from]
 		i++
 	}
+	if len(nodes) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedNodes(nodes)
 }
 
@@ -139,7 +145,7 @@ func (g *WeightedUndirectedGraph) Lines(uid, vid int64) graph.Lines {
 func (g *WeightedUndirectedGraph) LinesBetween(xid, yid int64) graph.Lines {
 	edge := g.lines[xid][yid]
 	if len(edge) == 0 {
-		return nil
+		return graph.Empty
 	}
 	var lines []graph.Line
 	seen := make(map[int64]struct{})
@@ -182,7 +188,7 @@ func (g *WeightedUndirectedGraph) Node(id int64) graph.Node {
 // Nodes returns all the nodes in the graph.
 func (g *WeightedUndirectedGraph) Nodes() graph.Nodes {
 	if len(g.nodes) == 0 {
-		return nil
+		return graph.Empty
 	}
 	nodes := make([]graph.Node, len(g.nodes))
 	i := 0
@@ -291,7 +297,7 @@ func (g *WeightedUndirectedGraph) WeightedEdgeBetween(xid, yid int64) graph.Weig
 // is a multi.Edge.
 func (g *WeightedUndirectedGraph) WeightedEdges() graph.WeightedEdges {
 	if len(g.lines) == 0 {
-		return nil
+		return graph.Empty
 	}
 	var edges []graph.WeightedEdge
 	seen := make(map[int64]struct{})
@@ -316,6 +322,9 @@ func (g *WeightedUndirectedGraph) WeightedEdges() graph.WeightedEdges {
 			}
 		}
 	}
+	if len(edges) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedWeightedEdges(edges)
 }
 
@@ -329,7 +338,7 @@ func (g *WeightedUndirectedGraph) WeightedLines(uid, vid int64) graph.WeightedLi
 func (g *WeightedUndirectedGraph) WeightedLinesBetween(xid, yid int64) graph.WeightedLines {
 	edge := g.lines[xid][yid]
 	if len(edge) == 0 {
-		return nil
+		return graph.Empty
 	}
 	var lines []graph.WeightedLine
 	seen := make(map[int64]struct{})

graph/multi/weighted_undirected_test.go

@@ -65,19 +65,19 @@ func TestWeightedUndirected(t *testing.T) {
 		testgraph.NodeExistence(t, weightedUndirectedBuilder)
 	})
 	t.Run("ReturnAdjacentNodes", func(t *testing.T) {
-		testgraph.ReturnAdjacentNodes(t, weightedUndirectedBuilder)
+		testgraph.ReturnAdjacentNodes(t, weightedUndirectedBuilder, true)
 	})
 	t.Run("ReturnAllLines", func(t *testing.T) {
-		testgraph.ReturnAllLines(t, weightedUndirectedBuilder)
+		testgraph.ReturnAllLines(t, weightedUndirectedBuilder, true)
 	})
 	t.Run("ReturnAllNodes", func(t *testing.T) {
-		testgraph.ReturnAllNodes(t, weightedUndirectedBuilder)
+		testgraph.ReturnAllNodes(t, weightedUndirectedBuilder, true)
 	})
 	t.Run("ReturnAllWeightedLines", func(t *testing.T) {
-		testgraph.ReturnAllWeightedLines(t, weightedUndirectedBuilder)
+		testgraph.ReturnAllWeightedLines(t, weightedUndirectedBuilder, true)
 	})
 	t.Run("ReturnNodeSlice", func(t *testing.T) {
-		testgraph.ReturnNodeSlice(t, weightedUndirectedBuilder)
+		testgraph.ReturnNodeSlice(t, weightedUndirectedBuilder, true)
 	})
 	t.Run("Weight", func(t *testing.T) {
 		testgraph.Weight(t, weightedUndirectedBuilder)

graph/multigraph.go

@@ -24,10 +24,14 @@ type Multigraph interface {
 	Node(id int64) Node
 
 	// Nodes returns all the nodes in the multigraph.
+	//
+	// Nodes must not return nil.
 	Nodes() Nodes
 
 	// From returns all nodes that can be reached directly
 	// from the node with the given ID.
+	//
+	// From must not return nil.
 	From(id int64) Nodes
 
 	// HasEdgeBetween returns whether an edge exists between
@@ -38,6 +42,8 @@ type Multigraph interface {
 	// vid, if any such lines exist and nil otherwise. The
 	// node v must be directly reachable from u as defined by
 	// the From method.
+	//
+	// Lines must not return nil.
 	Lines(uid, vid int64) Lines
 }
 
@@ -49,6 +55,8 @@ type WeightedMultigraph interface {
 	// with IDs uid and vid if any such lines exist and nil
 	// otherwise. The node v must be directly reachable
 	// from u as defined by the From method.
+	//
+	// WeightedLines must not return nil.
 	WeightedLines(uid, vid int64) WeightedLines
 }
 
@@ -58,6 +66,8 @@ type UndirectedMultigraph interface {
 
 	// LinesBetween returns the lines between nodes x and y
 	// with IDs xid and yid.
+	//
+	// LinesBetween must not return nil.
 	LinesBetween(xid, yid int64) Lines
 }
 
@@ -67,6 +77,8 @@ type WeightedUndirectedMultigraph interface {
 
 	// WeightedLinesBetween returns the lines between nodes
 	// x and y with IDs xid and yid.
+	//
+	// WeightedLinesBetween must not return nil.
 	WeightedLinesBetween(xid, yid int64) WeightedLines
 }
 
@@ -81,6 +93,8 @@ type DirectedMultigraph interface {
 
 	// To returns all nodes that can reach directly
 	// to the node with the given ID.
+	//
+	// To must not return nil.
 	To(id int64) Nodes
 }
 
@@ -95,6 +109,8 @@ type WeightedDirectedMultigraph interface {
 
 	// To returns all nodes that can reach directly
 	// to the node with the given ID.
+	//
+	// To must not return nil.
 	To(id int64) Nodes
 }
 

graph/nodes_edges.go

@@ -227,3 +227,40 @@ func WeightedLinesOf(it WeightedLines) []WeightedLine {
 	}
 	return l
 }
+
+// Empty is an empty set of nodes, edges or lines. It should be used when
+// a graph returns a zero-length Iterator. Empty implements the slicer
+// interfaces for nodes, edges and lines, returning nil for each of these.
+const Empty = nothing
+
+var (
+	_ Iterator           = Empty
+	_ Nodes              = Empty
+	_ NodeSlicer         = Empty
+	_ Edges              = Empty
+	_ EdgeSlicer         = Empty
+	_ WeightedEdges      = Empty
+	_ WeightedEdgeSlicer = Empty
+	_ Lines              = Empty
+	_ LineSlicer         = Empty
+	_ WeightedLines      = Empty
+	_ WeightedLineSlicer = Empty
+)
+
+const nothing = empty(true)
+
+type empty bool
+
+func (empty) Next() bool                        { return false }
+func (empty) Len() int                          { return 0 }
+func (empty) Reset()                            {}
+func (empty) Node() Node                        { return nil }
+func (empty) NodeSlice() []Node                 { return nil }
+func (empty) Edge() Edge                        { return nil }
+func (empty) EdgeSlice() []Edge                 { return nil }
+func (empty) WeightedEdge() WeightedEdge        { return nil }
+func (empty) WeightedEdgeSlice() []WeightedEdge { return nil }
+func (empty) Line() Line                        { return nil }
+func (empty) LineSlice() []Line                 { return nil }
+func (empty) WeightedLine() WeightedLine        { return nil }
+func (empty) WeightedLineSlice() []WeightedLine { return nil }

graph/path/internal/testgraphs/grid.go

@@ -169,7 +169,7 @@ func (g *Grid) NodeAt(r, c int) graph.Node {
 // ends of an edge must be open.
 func (g *Grid) From(uid int64) graph.Nodes {
 	if !g.HasOpen(uid) {
-		return nil
+		return graph.Empty
 	}
 	nr, nc := g.RowCol(uid)
 	var to []graph.Node
@@ -180,6 +180,9 @@ func (g *Grid) From(uid int64) graph.Nodes {
 			}
 		}
 	}
+	if len(to) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedNodes(to)
 }
 

graph/path/internal/testgraphs/limited.go

@@ -178,7 +178,7 @@ func (l *LimitedVisionGrid) has(id int64) bool {
 // From returns nodes that are optimistically reachable from u.
 func (l *LimitedVisionGrid) From(uid int64) graph.Nodes {
 	if !l.has(uid) {
-		return nil
+		return graph.Empty
 	}
 
 	nr, nc := l.RowCol(uid)
@@ -190,6 +190,9 @@ func (l *LimitedVisionGrid) From(uid int64) graph.Nodes {
 			}
 		}
 	}
+	if len(to) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedNodes(to)
 }
 

graph/simple/dense_directed_matrix.go

@@ -93,13 +93,16 @@ func (g *DirectedMatrix) Edges() graph.Edges {
 			}
 		}
 	}
+	if len(edges) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedEdges(edges)
 }
 
 // From returns all nodes in g that can be reached directly from n.
 func (g *DirectedMatrix) From(id int64) graph.Nodes {
 	if !g.has(id) {
-		return nil
+		return graph.Empty
 	}
 	var nodes []graph.Node
 	_, c := g.mat.Dims()
@@ -112,6 +115,9 @@ func (g *DirectedMatrix) From(id int64) graph.Nodes {
 			nodes = append(nodes, g.Node(int64(j)))
 		}
 	}
+	if len(nodes) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedNodes(nodes)
 }
 
@@ -169,6 +175,7 @@ func (g *DirectedMatrix) Nodes() graph.Nodes {
 		return iterator.NewOrderedNodes(nodes)
 	}
 	r, _ := g.mat.Dims()
+	// Matrix graphs must have at least one node.
 	return iterator.NewImplicitNodes(0, r, newSimpleNode)
 }
 
@@ -224,7 +231,7 @@ func (g *DirectedMatrix) setWeightedEdge(e graph.Edge, weight float64) {
 // To returns all nodes in g that can reach directly to n.
 func (g *DirectedMatrix) To(id int64) graph.Nodes {
 	if !g.has(id) {
-		return nil
+		return graph.Empty
 	}
 	var nodes []graph.Node
 	r, _ := g.mat.Dims()
@@ -237,6 +244,9 @@ func (g *DirectedMatrix) To(id int64) graph.Nodes {
 			nodes = append(nodes, g.Node(int64(i)))
 		}
 	}
+	if len(nodes) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedNodes(nodes)
 }
 
@@ -279,6 +289,9 @@ func (g *DirectedMatrix) WeightedEdges() graph.WeightedEdges {
 			}
 		}
 	}
+	if len(edges) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedWeightedEdges(edges)
 }
 

graph/simple/dense_undirected_matrix.go

@@ -95,13 +95,16 @@ func (g *UndirectedMatrix) Edges() graph.Edges {
 			}
 		}
 	}
+	if len(edges) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedEdges(edges)
 }
 
 // From returns all nodes in g that can be reached directly from n.
 func (g *UndirectedMatrix) From(id int64) graph.Nodes {
 	if !g.has(id) {
-		return nil
+		return graph.Empty
 	}
 	var nodes []graph.Node
 	r := g.mat.Symmetric()
@@ -114,6 +117,9 @@ func (g *UndirectedMatrix) From(id int64) graph.Nodes {
 			nodes = append(nodes, g.Node(int64(i)))
 		}
 	}
+	if len(nodes) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedNodes(nodes)
 }
 
@@ -156,6 +162,7 @@ func (g *UndirectedMatrix) Nodes() graph.Nodes {
 		return iterator.NewOrderedNodes(nodes)
 	}
 	r := g.mat.Symmetric()
+	// Matrix graphs must have at least one node.
 	return iterator.NewImplicitNodes(0, r, newSimpleNode)
 }
 
@@ -249,6 +256,9 @@ func (g *UndirectedMatrix) WeightedEdges() graph.WeightedEdges {
 			}
 		}
 	}
+	if len(edges) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedWeightedEdges(edges)
 }
 

graph/simple/densegraph_test.go

@@ -73,25 +73,25 @@ func TestDirectedMatrix(t *testing.T) {
 		testgraph.NodeExistence(t, directedMatrixBuilder)
 	})
 	t.Run("ReturnAdjacentNodes", func(t *testing.T) {
-		testgraph.ReturnAdjacentNodes(t, directedMatrixBuilder)
+		testgraph.ReturnAdjacentNodes(t, directedMatrixBuilder, true)
 	})
 	t.Run("ReturnAllEdges", func(t *testing.T) {
-		testgraph.ReturnAllEdges(t, directedMatrixBuilder)
+		testgraph.ReturnAllEdges(t, directedMatrixBuilder, true)
 	})
 	t.Run("ReturnAllNodes", func(t *testing.T) {
-		testgraph.ReturnAllNodes(t, directedMatrixBuilder)
+		testgraph.ReturnAllNodes(t, directedMatrixBuilder, true)
 	})
 	t.Run("ReturnAllWeightedEdges", func(t *testing.T) {
-		testgraph.ReturnAllWeightedEdges(t, directedMatrixBuilder)
+		testgraph.ReturnAllWeightedEdges(t, directedMatrixBuilder, true)
 	})
 	t.Run("ReturnEdgeSlice", func(t *testing.T) {
-		testgraph.ReturnEdgeSlice(t, directedMatrixBuilder)
+		testgraph.ReturnEdgeSlice(t, directedMatrixBuilder, true)
 	})
 	t.Run("ReturnWeightedEdgeSlice", func(t *testing.T) {
-		testgraph.ReturnWeightedEdgeSlice(t, directedMatrixBuilder)
+		testgraph.ReturnWeightedEdgeSlice(t, directedMatrixBuilder, true)
 	})
 	t.Run("ReturnNodeSlice", func(t *testing.T) {
-		testgraph.ReturnNodeSlice(t, directedMatrixBuilder)
+		testgraph.ReturnNodeSlice(t, directedMatrixBuilder, true)
 	})
 	t.Run("Weight", func(t *testing.T) {
 		testgraph.Weight(t, directedMatrixBuilder)
@@ -142,25 +142,25 @@ func TestDirectedMatrixFrom(t *testing.T) {
 		testgraph.NodeExistence(t, directedMatrixFromBuilder)
 	})
 	t.Run("ReturnAdjacentNodes", func(t *testing.T) {
-		testgraph.ReturnAdjacentNodes(t, directedMatrixFromBuilder)
+		testgraph.ReturnAdjacentNodes(t, directedMatrixFromBuilder, true)
 	})
 	t.Run("ReturnAllEdges", func(t *testing.T) {
-		testgraph.ReturnAllEdges(t, directedMatrixFromBuilder)
+		testgraph.ReturnAllEdges(t, directedMatrixFromBuilder, true)
 	})
 	t.Run("ReturnAllNodes", func(t *testing.T) {
-		testgraph.ReturnAllNodes(t, directedMatrixFromBuilder)
+		testgraph.ReturnAllNodes(t, directedMatrixFromBuilder, true)
 	})
 	t.Run("ReturnAllWeightedEdges", func(t *testing.T) {
-		testgraph.ReturnAllWeightedEdges(t, directedMatrixFromBuilder)
+		testgraph.ReturnAllWeightedEdges(t, directedMatrixFromBuilder, true)
 	})
 	t.Run("ReturnEdgeSlice", func(t *testing.T) {
-		testgraph.ReturnEdgeSlice(t, directedMatrixFromBuilder)
+		testgraph.ReturnEdgeSlice(t, directedMatrixFromBuilder, true)
 	})
 	t.Run("ReturnWeightedEdgeSlice", func(t *testing.T) {
-		testgraph.ReturnWeightedEdgeSlice(t, directedMatrixFromBuilder)
+		testgraph.ReturnWeightedEdgeSlice(t, directedMatrixFromBuilder, true)
 	})
 	t.Run("ReturnNodeSlice", func(t *testing.T) {
-		testgraph.ReturnNodeSlice(t, directedMatrixFromBuilder)
+		testgraph.ReturnNodeSlice(t, directedMatrixFromBuilder, true)
 	})
 	t.Run("Weight", func(t *testing.T) {
 		testgraph.Weight(t, directedMatrixFromBuilder)
@@ -211,25 +211,25 @@ func TestUnirectedMatrix(t *testing.T) {
 		testgraph.NodeExistence(t, undirectedMatrixBuilder)
 	})
 	t.Run("ReturnAdjacentNodes", func(t *testing.T) {
-		testgraph.ReturnAdjacentNodes(t, undirectedMatrixBuilder)
+		testgraph.ReturnAdjacentNodes(t, undirectedMatrixBuilder, true)
 	})
 	t.Run("ReturnAllEdges", func(t *testing.T) {
-		testgraph.ReturnAllEdges(t, undirectedMatrixBuilder)
+		testgraph.ReturnAllEdges(t, undirectedMatrixBuilder, true)
 	})
 	t.Run("ReturnAllNodes", func(t *testing.T) {
-		testgraph.ReturnAllNodes(t, undirectedMatrixBuilder)
+		testgraph.ReturnAllNodes(t, undirectedMatrixBuilder, true)
 	})
 	t.Run("ReturnAllWeightedEdges", func(t *testing.T) {
-		testgraph.ReturnAllWeightedEdges(t, undirectedMatrixBuilder)
+		testgraph.ReturnAllWeightedEdges(t, undirectedMatrixBuilder, true)
 	})
 	t.Run("ReturnEdgeSlice", func(t *testing.T) {
-		testgraph.ReturnEdgeSlice(t, undirectedMatrixBuilder)
+		testgraph.ReturnEdgeSlice(t, undirectedMatrixBuilder, true)
 	})
 	t.Run("ReturnWeightedEdgeSlice", func(t *testing.T) {
-		testgraph.ReturnWeightedEdgeSlice(t, undirectedMatrixBuilder)
+		testgraph.ReturnWeightedEdgeSlice(t, undirectedMatrixBuilder, true)
 	})
 	t.Run("ReturnNodeSlice", func(t *testing.T) {
-		testgraph.ReturnNodeSlice(t, undirectedMatrixBuilder)
+		testgraph.ReturnNodeSlice(t, undirectedMatrixBuilder, true)
 	})
 	t.Run("Weight", func(t *testing.T) {
 		testgraph.Weight(t, undirectedMatrixBuilder)
@@ -280,25 +280,25 @@ func TestUndirectedMatrixFrom(t *testing.T) {
 		testgraph.NodeExistence(t, undirectedMatrixFromBuilder)
 	})
 	t.Run("ReturnAdjacentNodes", func(t *testing.T) {
-		testgraph.ReturnAdjacentNodes(t, undirectedMatrixFromBuilder)
+		testgraph.ReturnAdjacentNodes(t, undirectedMatrixFromBuilder, true)
 	})
 	t.Run("ReturnAllEdges", func(t *testing.T) {
-		testgraph.ReturnAllEdges(t, undirectedMatrixFromBuilder)
+		testgraph.ReturnAllEdges(t, undirectedMatrixFromBuilder, true)
 	})
 	t.Run("ReturnAllNodes", func(t *testing.T) {
-		testgraph.ReturnAllNodes(t, undirectedMatrixFromBuilder)
+		testgraph.ReturnAllNodes(t, undirectedMatrixFromBuilder, true)
 	})
 	t.Run("ReturnAllWeightedEdges", func(t *testing.T) {
-		testgraph.ReturnAllWeightedEdges(t, undirectedMatrixFromBuilder)
+		testgraph.ReturnAllWeightedEdges(t, undirectedMatrixFromBuilder, true)
 	})
 	t.Run("ReturnEdgeSlice", func(t *testing.T) {
-		testgraph.ReturnEdgeSlice(t, undirectedMatrixFromBuilder)
+		testgraph.ReturnEdgeSlice(t, undirectedMatrixFromBuilder, true)
 	})
 	t.Run("ReturnWeightedEdgeSlice", func(t *testing.T) {
-		testgraph.ReturnWeightedEdgeSlice(t, undirectedMatrixFromBuilder)
+		testgraph.ReturnWeightedEdgeSlice(t, undirectedMatrixFromBuilder, true)
 	})
 	t.Run("ReturnNodeSlice", func(t *testing.T) {
-		testgraph.ReturnNodeSlice(t, undirectedMatrixFromBuilder)
+		testgraph.ReturnNodeSlice(t, undirectedMatrixFromBuilder, true)
 	})
 	t.Run("Weight", func(t *testing.T) {
 		testgraph.Weight(t, undirectedMatrixFromBuilder)

graph/simple/directed.go

@@ -72,13 +72,16 @@ func (g *DirectedGraph) Edges() graph.Edges {
 			edges = append(edges, e)
 		}
 	}
+	if len(edges) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedEdges(edges)
 }
 
 // From returns all nodes in g that can be reached directly from n.
 func (g *DirectedGraph) From(id int64) graph.Nodes {
 	if _, ok := g.from[id]; !ok {
-		return nil
+		return graph.Empty
 	}
 
 	from := make([]graph.Node, len(g.from[id]))
@@ -87,6 +90,9 @@ func (g *DirectedGraph) From(id int64) graph.Nodes {
 		from[i] = g.nodes[vid]
 		i++
 	}
+	if len(from) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedNodes(from)
 }
 
@@ -134,7 +140,7 @@ func (g *DirectedGraph) Node(id int64) graph.Node {
 // Nodes returns all the nodes in the graph.
 func (g *DirectedGraph) Nodes() graph.Nodes {
 	if len(g.nodes) == 0 {
-		return nil
+		return graph.Empty
 	}
 	nodes := make([]graph.Node, len(g.nodes))
 	i := 0
@@ -213,7 +219,7 @@ func (g *DirectedGraph) SetEdge(e graph.Edge) {
 // To returns all nodes in g that can reach directly to n.
 func (g *DirectedGraph) To(id int64) graph.Nodes {
 	if _, ok := g.from[id]; !ok {
-		return nil
+		return graph.Empty
 	}
 
 	to := make([]graph.Node, len(g.to[id]))
@@ -222,5 +228,8 @@ func (g *DirectedGraph) To(id int64) graph.Nodes {
 		to[i] = g.nodes[uid]
 		i++
 	}
+	if len(to) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedNodes(to)
 }

graph/simple/directed_test.go

@@ -59,19 +59,19 @@ func TestDirected(t *testing.T) {
 		testgraph.NodeExistence(t, directedBuilder)
 	})
 	t.Run("ReturnAdjacentNodes", func(t *testing.T) {
-		testgraph.ReturnAdjacentNodes(t, directedBuilder)
+		testgraph.ReturnAdjacentNodes(t, directedBuilder, true)
 	})
 	t.Run("ReturnAllEdges", func(t *testing.T) {
-		testgraph.ReturnAllEdges(t, directedBuilder)
+		testgraph.ReturnAllEdges(t, directedBuilder, true)
 	})
 	t.Run("ReturnAllNodes", func(t *testing.T) {
-		testgraph.ReturnAllNodes(t, directedBuilder)
+		testgraph.ReturnAllNodes(t, directedBuilder, true)
 	})
 	t.Run("ReturnEdgeSlice", func(t *testing.T) {
-		testgraph.ReturnEdgeSlice(t, directedBuilder)
+		testgraph.ReturnEdgeSlice(t, directedBuilder, true)
 	})
 	t.Run("ReturnNodeSlice", func(t *testing.T) {
-		testgraph.ReturnNodeSlice(t, directedBuilder)
+		testgraph.ReturnNodeSlice(t, directedBuilder, true)
 	})
 }
 

graph/simple/doc.go

@@ -4,4 +4,6 @@
 
 // Package simple provides a suite of simple graph implementations satisfying
 // the gonum/graph interfaces.
+//
+// All types in simple return the graph.Empty value for empty iterators.
 package simple // import "gonum.org/v1/gonum/graph/simple"

graph/simple/undirected.go

@@ -69,7 +69,7 @@ func (g *UndirectedGraph) EdgeBetween(xid, yid int64) graph.Edge {
 // Edges returns all the edges in the graph.
 func (g *UndirectedGraph) Edges() graph.Edges {
 	if len(g.edges) == 0 {
-		return nil
+		return graph.Empty
 	}
 	var edges []graph.Edge
 	seen := make(map[[2]int64]struct{})
@@ -85,13 +85,16 @@ func (g *UndirectedGraph) Edges() graph.Edges {
 			edges = append(edges, e)
 		}
 	}
+	if len(edges) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedEdges(edges)
 }
 
 // From returns all nodes in g that can be reached directly from n.
 func (g *UndirectedGraph) From(id int64) graph.Nodes {
 	if _, ok := g.nodes[id]; !ok {
-		return nil
+		return graph.Empty
 	}
 
 	nodes := make([]graph.Node, len(g.edges[id]))
@@ -100,6 +103,9 @@ func (g *UndirectedGraph) From(id int64) graph.Nodes {
 		nodes[i] = g.nodes[from]
 		i++
 	}
+	if len(nodes) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedNodes(nodes)
 }
 
@@ -135,7 +141,7 @@ func (g *UndirectedGraph) Node(id int64) graph.Node {
 // Nodes returns all the nodes in the graph.
 func (g *UndirectedGraph) Nodes() graph.Nodes {
 	if len(g.nodes) == 0 {
-		return nil
+		return graph.Empty
 	}
 	nodes := make([]graph.Node, len(g.nodes))
 	i := 0

graph/simple/undirected_test.go

@@ -59,19 +59,19 @@ func TestUndirected(t *testing.T) {
 		testgraph.NodeExistence(t, undirectedBuilder)
 	})
 	t.Run("ReturnAdjacentNodes", func(t *testing.T) {
-		testgraph.ReturnAdjacentNodes(t, undirectedBuilder)
+		testgraph.ReturnAdjacentNodes(t, undirectedBuilder, true)
 	})
 	t.Run("ReturnAllEdges", func(t *testing.T) {
-		testgraph.ReturnAllEdges(t, undirectedBuilder)
+		testgraph.ReturnAllEdges(t, undirectedBuilder, true)
 	})
 	t.Run("ReturnAllNodes", func(t *testing.T) {
-		testgraph.ReturnAllNodes(t, undirectedBuilder)
+		testgraph.ReturnAllNodes(t, undirectedBuilder, true)
 	})
 	t.Run("ReturnEdgeSlice", func(t *testing.T) {
-		testgraph.ReturnEdgeSlice(t, undirectedBuilder)
+		testgraph.ReturnEdgeSlice(t, undirectedBuilder, true)
 	})
 	t.Run("ReturnNodeSlice", func(t *testing.T) {
-		testgraph.ReturnNodeSlice(t, undirectedBuilder)
+		testgraph.ReturnNodeSlice(t, undirectedBuilder, true)
 	})
 }
 

graph/simple/weighted_directed.go

@@ -76,13 +76,16 @@ func (g *WeightedDirectedGraph) Edges() graph.Edges {
 			edges = append(edges, e)
 		}
 	}
+	if len(edges) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedEdges(edges)
 }
 
 // From returns all nodes in g that can be reached directly from n.
 func (g *WeightedDirectedGraph) From(id int64) graph.Nodes {
 	if _, ok := g.from[id]; !ok {
-		return nil
+		return graph.Empty
 	}
 
 	from := make([]graph.Node, len(g.from[id]))
@@ -91,6 +94,9 @@ func (g *WeightedDirectedGraph) From(id int64) graph.Nodes {
 		from[i] = g.nodes[vid]
 		i++
 	}
+	if len(from) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedNodes(from)
 }
 
@@ -138,7 +144,7 @@ func (g *WeightedDirectedGraph) Node(id int64) graph.Node {
 // Nodes returns all the nodes in the graph.
 func (g *WeightedDirectedGraph) Nodes() graph.Nodes {
 	if len(g.from) == 0 {
-		return nil
+		return graph.Empty
 	}
 	nodes := make([]graph.Node, len(g.nodes))
 	i := 0
@@ -217,7 +223,7 @@ func (g *WeightedDirectedGraph) SetWeightedEdge(e graph.WeightedEdge) {
 // To returns all nodes in g that can reach directly to n.
 func (g *WeightedDirectedGraph) To(id int64) graph.Nodes {
 	if _, ok := g.from[id]; !ok {
-		return nil
+		return graph.Empty
 	}
 
 	to := make([]graph.Node, len(g.to[id]))
@@ -226,6 +232,9 @@ func (g *WeightedDirectedGraph) To(id int64) graph.Nodes {
 		to[i] = g.nodes[uid]
 		i++
 	}
+	if len(to) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedNodes(to)
 }
 
@@ -263,5 +272,8 @@ func (g *WeightedDirectedGraph) WeightedEdges() graph.WeightedEdges {
 			edges = append(edges, e)
 		}
 	}
+	if len(edges) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedWeightedEdges(edges)
 }

graph/simple/weighted_directed_test.go

@@ -59,25 +59,25 @@ func TestWeightedDirected(t *testing.T) {
 		testgraph.NodeExistence(t, weightedDirectedBuilder)
 	})
 	t.Run("ReturnAdjacentNodes", func(t *testing.T) {
-		testgraph.ReturnAdjacentNodes(t, weightedDirectedBuilder)
+		testgraph.ReturnAdjacentNodes(t, weightedDirectedBuilder, true)
 	})
 	t.Run("ReturnAllEdges", func(t *testing.T) {
-		testgraph.ReturnAllEdges(t, weightedDirectedBuilder)
+		testgraph.ReturnAllEdges(t, weightedDirectedBuilder, true)
 	})
 	t.Run("ReturnAllNodes", func(t *testing.T) {
-		testgraph.ReturnAllNodes(t, weightedDirectedBuilder)
+		testgraph.ReturnAllNodes(t, weightedDirectedBuilder, true)
 	})
 	t.Run("ReturnAllWeightedEdges", func(t *testing.T) {
-		testgraph.ReturnAllWeightedEdges(t, weightedDirectedBuilder)
+		testgraph.ReturnAllWeightedEdges(t, weightedDirectedBuilder, true)
 	})
 	t.Run("ReturnEdgeSlice", func(t *testing.T) {
-		testgraph.ReturnEdgeSlice(t, weightedDirectedBuilder)
+		testgraph.ReturnEdgeSlice(t, weightedDirectedBuilder, true)
 	})
 	t.Run("ReturnWeightedEdgeSlice", func(t *testing.T) {
-		testgraph.ReturnWeightedEdgeSlice(t, weightedDirectedBuilder)
+		testgraph.ReturnWeightedEdgeSlice(t, weightedDirectedBuilder, true)
 	})
 	t.Run("ReturnNodeSlice", func(t *testing.T) {
-		testgraph.ReturnNodeSlice(t, weightedDirectedBuilder)
+		testgraph.ReturnNodeSlice(t, weightedDirectedBuilder, true)
 	})
 	t.Run("Weight", func(t *testing.T) {
 		testgraph.Weight(t, weightedDirectedBuilder)

graph/simple/weighted_undirected.go

@@ -73,7 +73,7 @@ func (g *WeightedUndirectedGraph) EdgeBetween(xid, yid int64) graph.Edge {
 // Edges returns all the edges in the graph.
 func (g *WeightedUndirectedGraph) Edges() graph.Edges {
 	if len(g.edges) == 0 {
-		return nil
+		return graph.Empty
 	}
 	var edges []graph.Edge
 	seen := make(map[[2]int64]struct{})
@@ -89,13 +89,16 @@ func (g *WeightedUndirectedGraph) Edges() graph.Edges {
 			edges = append(edges, e)
 		}
 	}
+	if len(edges) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedEdges(edges)
 }
 
 // From returns all nodes in g that can be reached directly from n.
 func (g *WeightedUndirectedGraph) From(id int64) graph.Nodes {
 	if _, ok := g.nodes[id]; !ok {
-		return nil
+		return graph.Empty
 	}
 
 	nodes := make([]graph.Node, len(g.edges[id]))
@@ -104,6 +107,9 @@ func (g *WeightedUndirectedGraph) From(id int64) graph.Nodes {
 		nodes[i] = g.nodes[from]
 		i++
 	}
+	if len(nodes) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedNodes(nodes)
 }
 
@@ -139,7 +145,7 @@ func (g *WeightedUndirectedGraph) Node(id int64) graph.Node {
 // Nodes returns all the nodes in the graph.
 func (g *WeightedUndirectedGraph) Nodes() graph.Nodes {
 	if len(g.nodes) == 0 {
-		return nil
+		return graph.Empty
 	}
 	nodes := make([]graph.Node, len(g.nodes))
 	i := 0
@@ -257,5 +263,8 @@ func (g *WeightedUndirectedGraph) WeightedEdges() graph.WeightedEdges {
 			edges = append(edges, e)
 		}
 	}
+	if len(edges) == 0 {
+		return graph.Empty
+	}
 	return iterator.NewOrderedWeightedEdges(edges)
 }

graph/simple/weighted_undirected_test.go

@@ -59,25 +59,25 @@ func TestWeightedUndirected(t *testing.T) {
 		testgraph.NodeExistence(t, weightedUndirectedBuilder)
 	})
 	t.Run("ReturnAdjacentNodes", func(t *testing.T) {
-		testgraph.ReturnAdjacentNodes(t, weightedUndirectedBuilder)
+		testgraph.ReturnAdjacentNodes(t, weightedUndirectedBuilder, true)
 	})
 	t.Run("ReturnAllEdges", func(t *testing.T) {
-		testgraph.ReturnAllEdges(t, weightedUndirectedBuilder)
+		testgraph.ReturnAllEdges(t, weightedUndirectedBuilder, true)
 	})
 	t.Run("ReturnAllNodes", func(t *testing.T) {
-		testgraph.ReturnAllNodes(t, weightedUndirectedBuilder)
+		testgraph.ReturnAllNodes(t, weightedUndirectedBuilder, true)
 	})
 	t.Run("ReturnAllWeightedEdges", func(t *testing.T) {
-		testgraph.ReturnAllWeightedEdges(t, weightedUndirectedBuilder)
+		testgraph.ReturnAllWeightedEdges(t, weightedUndirectedBuilder, true)
 	})
 	t.Run("ReturnEdgeSlice", func(t *testing.T) {
-		testgraph.ReturnEdgeSlice(t, weightedUndirectedBuilder)
+		testgraph.ReturnEdgeSlice(t, weightedUndirectedBuilder, true)
 	})
 	t.Run("ReturnWeightedEdgeSlice", func(t *testing.T) {
-		testgraph.ReturnWeightedEdgeSlice(t, weightedUndirectedBuilder)
+		testgraph.ReturnWeightedEdgeSlice(t, weightedUndirectedBuilder, true)
 	})
 	t.Run("ReturnNodeSlice", func(t *testing.T) {
-		testgraph.ReturnNodeSlice(t, weightedUndirectedBuilder)
+		testgraph.ReturnNodeSlice(t, weightedUndirectedBuilder, true)
 	})
 	t.Run("Weight", func(t *testing.T) {
 		testgraph.Weight(t, weightedUndirectedBuilder)

graph/testgraph/testgraph.go

@@ -25,16 +25,23 @@ import (
 // compared with NaN-awareness, so they may be NaN when there is no edge
 // associated with the Weight call.
 
-// BUG(kortschak): The approach of using a nil return for empty sets of nodes
-// and edges used prior to the introduction of the graph.Iterator types does
-// not interact well with interfaces. For example, it is not possible to simply
-// determine that an iterator is empty by calling it.Len without guarding that
-// with a nil check. The validity of nil iterators may change depending on the
-// outcome of https://github.com/gonum/gonum/issues/614.
-func isValidIterator(graph.Iterator) bool {
-	// TODO(kortschak): Remove nil guards in iterator
-	// loops and slicer tests if this changes.
-	return true
+func isValidIterator(it graph.Iterator) bool {
+	return it != nil
+}
+
+func checkEmptyIterator(t *testing.T, it graph.Iterator, useEmpty bool) {
+	if it.Len() != 0 {
+		return
+	}
+	if it != graph.Empty {
+		if useEmpty {
+			t.Errorf("unexpected empty iterator: got:%T", it)
+			return
+		}
+		// Only log this since we say that a graph should
+		// return a graph.Empty when it is empty.
+		t.Logf("unexpected empty iterator: got:%T", it)
+	}
 }
 
 // A Builder function returns a graph constructed from the nodes, edges and
@@ -68,7 +75,9 @@ type matrixer interface {
 // ReturnAllNodes tests the constructed graph for the ability to return all
 // the nodes it claims it has used in its construction. This is a check of
 // the Nodes method of graph.Graph and the iterator that is returned.
-func ReturnAllNodes(t *testing.T, b Builder) {
+// If useEmpty is true, graph iterators will be checked for the use of
+// graph.Empty if they are empty.
+func ReturnAllNodes(t *testing.T, b Builder, useEmpty bool) {
 	for _, test := range testCases {
 		g, want, _, _, _, ok := b(test.nodes, test.edges, test.self, test.absent)
 		if !ok {
@@ -81,8 +90,9 @@ func ReturnAllNodes(t *testing.T, b Builder) {
 			t.Errorf("invalid iterator for test %q: got:%#v", test.name, it)
 			continue
 		}
+		checkEmptyIterator(t, it, useEmpty)
 		var got []graph.Node
-		for it != nil && it.Next() {
+		for it.Next() {
 			got = append(got, it.Node())
 		}
 
@@ -99,7 +109,9 @@ func ReturnAllNodes(t *testing.T, b Builder) {
 // the nodes it claims it has used in its construction using the NodeSlicer
 // interface. This is a check of the Nodes method of graph.Graph and the
 // iterator that is returned.
-func ReturnNodeSlice(t *testing.T, b Builder) {
+// If useEmpty is true, graph iterators will be checked for the use of
+// graph.Empty if they are empty.
+func ReturnNodeSlice(t *testing.T, b Builder, useEmpty bool) {
 	for _, test := range testCases {
 		g, want, _, _, _, ok := b(test.nodes, test.edges, test.self, test.absent)
 		if !ok {
@@ -112,6 +124,7 @@ func ReturnNodeSlice(t *testing.T, b Builder) {
 			t.Errorf("invalid iterator for test %q: got:%#v", test.name, it)
 			continue
 		}
+		checkEmptyIterator(t, it, useEmpty)
 		if it == nil {
 			continue
 		}
@@ -168,7 +181,9 @@ func NodeExistence(t *testing.T, b Builder) {
 // the Edges method of graph.Graph and the iterator that is returned.
 // ReturnAllEdges  also checks that the edge end nodes exist within the graph,
 // checking the Node method of graph.Graph.
-func ReturnAllEdges(t *testing.T, b Builder) {
+// If useEmpty is true, graph iterators will be checked for the use of
+// graph.Empty if they are empty.
+func ReturnAllEdges(t *testing.T, b Builder, useEmpty bool) {
 	for _, test := range testCases {
 		g, _, want, _, _, ok := b(test.nodes, test.edges, test.self, test.absent)
 		if !ok {
@@ -184,7 +199,8 @@ func ReturnAllEdges(t *testing.T, b Builder) {
 				t.Errorf("invalid iterator for test %q: got:%#v", test.name, it)
 				continue
 			}
-			for it != nil && it.Next() {
+			checkEmptyIterator(t, it, useEmpty)
+			for it.Next() {
 				e := it.Edge()
 				got = append(got, e)
 				if g.Edge(e.From().ID(), e.To().ID()) == nil {
@@ -212,7 +228,9 @@ func ReturnAllEdges(t *testing.T, b Builder) {
 // interface. This is a check of the Edges method of graph.Graph and the
 // iterator that is returned. ReturnEdgeSlice also checks that the edge end
 // nodes exist within the graph, checking the Node method of graph.Graph.
-func ReturnEdgeSlice(t *testing.T, b Builder) {
+// If useEmpty is true, graph iterators will be checked for the use of
+// graph.Empty if they are empty.
+func ReturnEdgeSlice(t *testing.T, b Builder, useEmpty bool) {
 	for _, test := range testCases {
 		g, _, want, _, _, ok := b(test.nodes, test.edges, test.self, test.absent)
 		if !ok {
@@ -228,6 +246,7 @@ func ReturnEdgeSlice(t *testing.T, b Builder) {
 				t.Errorf("invalid iterator for test %q: got:%#v", test.name, it)
 				continue
 			}
+			checkEmptyIterator(t, it, useEmpty)
 			if it == nil {
 				continue
 			}
@@ -267,7 +286,9 @@ func ReturnEdgeSlice(t *testing.T, b Builder) {
 //
 // The edges used within and returned by the Builder function should be
 // graph.Line. The edge parameter passed to b will contain only graph.Line.
-func ReturnAllLines(t *testing.T, b Builder) {
+// If useEmpty is true, graph iterators will be checked for the use of
+// graph.Empty if they are empty.
+func ReturnAllLines(t *testing.T, b Builder, useEmpty bool) {
 	for _, test := range testCases {
 		g, _, want, _, _, ok := b(test.nodes, test.edges, test.self, test.absent)
 		if !ok {
@@ -283,6 +304,7 @@ func ReturnAllLines(t *testing.T, b Builder) {
 				t.Errorf("invalid iterator for test %q: got:%#v", test.name, it)
 				continue
 			}
+			checkEmptyIterator(t, it, useEmpty)
 			for _, e := range graph.EdgesOf(it) {
 				if g.Edge(e.From().ID(), e.To().ID()) == nil {
 					t.Errorf("missing edge for test %q: %v", test.name, e)
@@ -294,11 +316,11 @@ func ReturnAllLines(t *testing.T, b Builder) {
 				// and graph.Edges.
 				switch lit := e.(type) {
 				case graph.Lines:
-					for lit != nil && lit.Next() {
+					for lit.Next() {
 						got = append(got, lit.Line())
 					}
 				case graph.WeightedLines:
-					for lit != nil && lit.Next() {
+					for lit.Next() {
 						got = append(got, lit.WeightedLine())
 					}
 				default:
@@ -331,7 +353,9 @@ func ReturnAllLines(t *testing.T, b Builder) {
 // The edges used within and returned by the Builder function should be
 // graph.WeightedEdge. The edge parameter passed to b will contain only
 // graph.WeightedEdge.
-func ReturnAllWeightedEdges(t *testing.T, b Builder) {
+// If useEmpty is true, graph iterators will be checked for the use of
+// graph.Empty if they are empty.
+func ReturnAllWeightedEdges(t *testing.T, b Builder, useEmpty bool) {
 	for _, test := range testCases {
 		g, _, want, _, _, ok := b(test.nodes, test.edges, test.self, test.absent)
 		if !ok {
@@ -347,7 +371,8 @@ func ReturnAllWeightedEdges(t *testing.T, b Builder) {
 				t.Errorf("invalid iterator for test %q: got:%#v", test.name, it)
 				continue
 			}
-			for it != nil && it.Next() {
+			checkEmptyIterator(t, it, useEmpty)
+			for it.Next() {
 				e := it.WeightedEdge()
 				got = append(got, e)
 				switch g := g.(type) {
@@ -388,7 +413,9 @@ func ReturnAllWeightedEdges(t *testing.T, b Builder) {
 // The edges used within and returned by the Builder function should be
 // graph.WeightedEdge. The edge parameter passed to b will contain only
 // graph.WeightedEdge.
-func ReturnWeightedEdgeSlice(t *testing.T, b Builder) {
+// If useEmpty is true, graph iterators will be checked for the use of
+// graph.Empty if they are empty.
+func ReturnWeightedEdgeSlice(t *testing.T, b Builder, useEmpty bool) {
 	for _, test := range testCases {
 		g, _, want, _, _, ok := b(test.nodes, test.edges, test.self, test.absent)
 		if !ok {
@@ -404,6 +431,7 @@ func ReturnWeightedEdgeSlice(t *testing.T, b Builder) {
 				t.Errorf("invalid iterator for test %q: got:%#v", test.name, it)
 				continue
 			}
+			checkEmptyIterator(t, it, useEmpty)
 			s, ok := it.(graph.WeightedEdgeSlicer)
 			if !ok {
 				t.Errorf("invalid type for test %T: cannot return weighted edge slice", g)
@@ -442,7 +470,9 @@ func ReturnWeightedEdgeSlice(t *testing.T, b Builder) {
 // The edges used within and returned by the Builder function should be
 // graph.WeightedLine. The edge parameter passed to b will contain only
 // graph.WeightedLine.
-func ReturnAllWeightedLines(t *testing.T, b Builder) {
+// If useEmpty is true, graph iterators will be checked for the use of
+// graph.Empty if they are empty.
+func ReturnAllWeightedLines(t *testing.T, b Builder, useEmpty bool) {
 	for _, test := range testCases {
 		g, _, want, _, _, ok := b(test.nodes, test.edges, test.self, test.absent)
 		if !ok {
@@ -458,6 +488,7 @@ func ReturnAllWeightedLines(t *testing.T, b Builder) {
 				t.Errorf("invalid iterator for test %q: got:%#v", test.name, it)
 				continue
 			}
+			checkEmptyIterator(t, it, useEmpty)
 			for _, e := range graph.WeightedEdgesOf(it) {
 				if g.Edge(e.From().ID(), e.To().ID()) == nil {
 					t.Errorf("missing edge for test %q: %v", test.name, e)
@@ -469,11 +500,11 @@ func ReturnAllWeightedLines(t *testing.T, b Builder) {
 				// and graph.Edges.
 				switch lit := e.(type) {
 				case graph.Lines:
-					for lit != nil && lit.Next() {
+					for lit.Next() {
 						got = append(got, lit.Line())
 					}
 				case graph.WeightedLines:
-					for lit != nil && lit.Next() {
+					for lit.Next() {
 						got = append(got, lit.WeightedLine())
 					}
 				default:
@@ -602,7 +633,9 @@ func EdgeExistence(t *testing.T, b Builder) {
 // within the graph, checking the Node, Edge, EdgeBetween and HasEdgeBetween
 // methods of graph.Graph, the EdgeBetween method of graph.Undirected and the
 // HasEdgeFromTo method of graph.Directed.
-func ReturnAdjacentNodes(t *testing.T, b Builder) {
+// If useEmpty is true, graph iterators will be checked for the use of
+// graph.Empty if they are empty.
+func ReturnAdjacentNodes(t *testing.T, b Builder, useEmpty bool) {
 	for _, test := range testCases {
 		g, nodes, edges, _, _, ok := b(test.nodes, test.edges, test.self, test.absent)
 		if !ok {
@@ -620,7 +653,12 @@ func ReturnAdjacentNodes(t *testing.T, b Builder) {
 				// Test forward.
 				u := x
 				it := g.From(u.ID())
-				for i := 0; it != nil && it.Next(); i++ {
+				if !isValidIterator(it) {
+					t.Errorf("invalid iterator for test %q: got:%#v", test.name, it)
+					continue
+				}
+				checkEmptyIterator(t, it, useEmpty)
+				for i := 0; it.Next(); i++ {
 					v := it.Node()
 					if i == 0 && g.Node(u.ID()) == nil {
 						t.Errorf("missing from node for test %q: %v", test.name, u.ID())
@@ -645,7 +683,12 @@ func ReturnAdjacentNodes(t *testing.T, b Builder) {
 				// Test backward.
 				v := x
 				it = g.To(v.ID())
-				for i := 0; it != nil && it.Next(); i++ {
+				if !isValidIterator(it) {
+					t.Errorf("invalid iterator for test %q: got:%#v", test.name, it)
+					continue
+				}
+				checkEmptyIterator(t, it, useEmpty)
+				for i := 0; it.Next(); i++ {
 					u := it.Node()
 					if i == 0 && g.Node(v.ID()) == nil {
 						t.Errorf("missing to node for test %q: %v", test.name, v.ID())
@@ -673,7 +716,12 @@ func ReturnAdjacentNodes(t *testing.T, b Builder) {
 			case graph.Undirected:
 				u := x
 				it := g.From(u.ID())
-				for i := 0; it != nil && it.Next(); i++ {
+				if !isValidIterator(it) {
+					t.Errorf("invalid iterator for test %q: got:%#v", test.name, it)
+					continue
+				}
+				checkEmptyIterator(t, it, useEmpty)
+				for i := 0; it.Next(); i++ {
 					v := it.Node()
 					if i == 0 && g.Node(u.ID()) == nil {
 						t.Errorf("missing from node for test %q: %v", test.name, u.ID())
@@ -699,7 +747,12 @@ func ReturnAdjacentNodes(t *testing.T, b Builder) {
 			default:
 				u := x
 				it := g.From(u.ID())
-				for i := 0; it != nil && it.Next(); i++ {
+				if !isValidIterator(it) {
+					t.Errorf("invalid iterator for test %q: got:%#v", test.name, it)
+					continue
+				}
+				checkEmptyIterator(t, it, useEmpty)
+				for i := 0; it.Next(); i++ {
 					v := it.Node()
 					if i == 0 && g.Node(u.ID()) == nil {
 						t.Errorf("missing from node for test %q: %v", test.name, u.ID())

graph/topo/johnson_cycles.go

@@ -252,7 +252,7 @@ func (g johnsonGraph) Nodes() graph.Nodes {
 func (g johnsonGraph) From(id int64) graph.Nodes {
 	adj := g.succ[id]
 	if len(adj) == 0 {
-		return nil
+		return graph.Empty
 	}
 	succ := make([]graph.Node, 0, len(adj))
 	for id := range adj {