diff --git a/dag/graph.go b/dag/graph.go
index 7fac2a534..41d766f40 100644
--- a/dag/graph.go
+++ b/dag/graph.go
@@ -82,6 +82,11 @@ func (g *Graph) Replace(original, replacement Vertex) bool {
 		return false
 	}
 
+	// If they're the same, then don't do anything
+	if original == replacement {
+		return true
+	}
+
 	// Add our new vertex, then copy all the edges
 	g.Add(replacement)
 	for _, target := range g.DownEdges(original).List() {
diff --git a/dag/graph_test.go b/dag/graph_test.go
index e67535659..8dd05e95e 100644
--- a/dag/graph_test.go
+++ b/dag/graph_test.go
@@ -63,6 +63,22 @@ func TestGraph_replace(t *testing.T) {
 	}
 }
 
+func TestGraph_replaceSelf(t *testing.T) {
+	var g Graph
+	g.Add(1)
+	g.Add(2)
+	g.Add(3)
+	g.Connect(BasicEdge(1, 2))
+	g.Connect(BasicEdge(2, 3))
+	g.Replace(2, 2)
+
+	actual := strings.TrimSpace(g.String())
+	expected := strings.TrimSpace(testGraphReplaceSelfStr)
+	if actual != expected {
+		t.Fatalf("bad: %s", actual)
+	}
+}
+
 const testGraphBasicStr = `
 1
   3
@@ -88,3 +104,11 @@ const testGraphReplaceStr = `
 42
   3
 `
+
+const testGraphReplaceSelfStr = `
+1
+  2
+2
+  3
+3
+`