diff --git a/graph/encoding/dot/decode.go b/graph/encoding/dot/decode.go
index ccc2868d..a001bbd2 100644
--- a/graph/encoding/dot/decode.go
+++ b/graph/encoding/dot/decode.go
@@ -54,6 +54,9 @@ func copyGraph(dst encoding.Builder, src *ast.Graph) (err error) {
 		directed: src.Directed,
 		ids:      make(map[string]graph.Node),
 	}
+	if dst, ok := dst.(DOTIDSetter); ok {
+		dst.SetDOTID(src.ID)
+	}
 	if a, ok := dst.(AttributeSetters); ok {
 		gen.graphAttr, gen.nodeAttr, gen.edgeAttr = a.DOTAttributeSetters()
 	}
diff --git a/graph/encoding/dot/decode_test.go b/graph/encoding/dot/decode_test.go
index d05b0507..c345c427 100644
--- a/graph/encoding/dot/decode_test.go
+++ b/graph/encoding/dot/decode_test.go
@@ -26,6 +26,14 @@ func TestRoundTrip(t *testing.T) {
 			want:     undirected,
 			directed: false,
 		},
+		{
+			want:     directedID,
+			directed: true,
+		},
+		{
+			want:     undirectedID,
+			directed: false,
+		},
 	}
 	for i, g := range golden {
 		var dst encoding.Builder
@@ -94,6 +102,24 @@ const undirected = `graph {
 	A -- B [label="baz 2"];
 }`
 
+const directedID = `digraph G {
+	// Node definitions.
+	A;
+	B;
+
+	// Edge definitions.
+	A -> B;
+}`
+
+const undirectedID = `graph H {
+	// Node definitions.
+	A;
+	B;
+
+	// Edge definitions.
+	A -- B;
+}`
+
 // Below follows a minimal implementation of a graph capable of validating the
 // round-trip encoding and decoding of DOT graphs with nodes and edges
 // containing DOT attributes.
@@ -101,9 +127,11 @@ const undirected = `graph {
 // dotDirectedGraph extends simple.DirectedGraph to add NewNode and NewEdge
 // methods for creating user-defined nodes and edges.
 //
-// dotDirectedGraph implements the dot.Builder interface.
+// dotDirectedGraph implements the encoding.Builder and the dot.Graph
+// interfaces.
 type dotDirectedGraph struct {
 	*simple.DirectedGraph
+	id                string
 	graph, node, edge attributes
 }
 
@@ -133,12 +161,24 @@ func (g *dotDirectedGraph) DOTAttributeSetters() (graph, node, edge encoding.Att
 	return &g.graph, &g.node, &g.edge
 }
 
+// SetDOTID sets the DOT ID of the graph.
+func (g *dotDirectedGraph) SetDOTID(id string) {
+	g.id = id
+}
+
+// DOTID returns the DOT ID of the graph.
+func (g *dotDirectedGraph) DOTID() string {
+	return g.id
+}
+
 // dotUndirectedGraph extends simple.UndirectedGraph to add NewNode and NewEdge
 // methods for creating user-defined nodes and edges.
 //
-// dotUndirectedGraph implements the dot.Builder interface.
+// dotUndirectedGraph implements the encoding.Builder and the dot.Graph
+// interfaces.
 type dotUndirectedGraph struct {
 	*simple.UndirectedGraph
+	id                string
 	graph, node, edge attributes
 }
 
@@ -168,6 +208,16 @@ func (g *dotUndirectedGraph) DOTAttributeSetters() (graph, node, edge encoding.A
 	return &g.graph, &g.node, &g.edge
 }
 
+// SetDOTID sets the DOT ID of the graph.
+func (g *dotUndirectedGraph) SetDOTID(id string) {
+	g.id = id
+}
+
+// DOTID returns the DOT ID of the graph.
+func (g *dotUndirectedGraph) DOTID() string {
+	return g.id
+}
+
 // dotNode extends simple.Node with a label field to test round-trip encoding
 // and decoding of node DOT label attributes.
 type dotNode struct {