diff --git a/internal/dag/dag.go b/internal/dag/dag.go
index 5aca57944..6da10df51 100644
--- a/internal/dag/dag.go
+++ b/internal/dag/dag.go
@@ -88,9 +88,7 @@ func (g *AcyclicGraph) Root() (Vertex, error) {
 // same graph with only a single edge between A and B, and a single edge
 // between B and C.
 //
-// The graph must be valid for this operation to behave properly. If
-// Validate() returns an error, the behavior is undefined and the results
-// will likely be unexpected.
+// The graph must be free of cycles for this operation to behave properly.
 //
 // Complexity: O(V(V+E)), or asymptotically O(VE)
 func (g *AcyclicGraph) TransitiveReduction() {
@@ -145,6 +143,8 @@ func (g *AcyclicGraph) Validate() error {
 	return err
 }
 
+// Cycles reports any cycles between graph nodes.
+// Self-referencing nodes are not reported, and must be detected separately.
 func (g *AcyclicGraph) Cycles() [][]Vertex {
 	var cycles [][]Vertex
 	for _, cycle := range StronglyConnected(&g.Graph) {
@@ -180,6 +180,8 @@ type vertexAtDepth struct {
 
 // DepthFirstWalk does a depth-first walk of the graph starting from
 // the vertices in start.
+// The algorithm used here does not do a complete topological sort. To ensure
+// correct overall ordering run TransitiveReduction first.
 func (g *AcyclicGraph) DepthFirstWalk(start Set, f DepthWalkFunc) error {
 	seen := make(map[Vertex]struct{})
 	frontier := make([]*vertexAtDepth, 0, len(start))
@@ -219,6 +221,8 @@ func (g *AcyclicGraph) DepthFirstWalk(start Set, f DepthWalkFunc) error {
 
 // ReverseDepthFirstWalk does a depth-first walk _up_ the graph starting from
 // the vertices in start.
+// The algorithm used here does not do a complete topological sort. To ensure
+// correct overall ordering run TransitiveReduction first.
 func (g *AcyclicGraph) ReverseDepthFirstWalk(start Set, f DepthWalkFunc) error {
 	seen := make(map[Vertex]struct{})
 	frontier := make([]*vertexAtDepth, 0, len(start))
diff --git a/internal/dag/dag_test.go b/internal/dag/dag_test.go
index 9c8cdb794..75cfb86ff 100644
--- a/internal/dag/dag_test.go
+++ b/internal/dag/dag_test.go
@@ -99,6 +99,38 @@ func TestAyclicGraphTransReduction_more(t *testing.T) {
 	}
 }
 
+func TestAyclicGraphTransReduction_multipleRoots(t *testing.T) {
+	var g AcyclicGraph
+	g.Add(1)
+	g.Add(2)
+	g.Add(3)
+	g.Add(4)
+	g.Connect(BasicEdge(1, 2))
+	g.Connect(BasicEdge(1, 3))
+	g.Connect(BasicEdge(1, 4))
+	g.Connect(BasicEdge(2, 3))
+	g.Connect(BasicEdge(2, 4))
+	g.Connect(BasicEdge(3, 4))
+
+	g.Add(5)
+	g.Add(6)
+	g.Add(7)
+	g.Add(8)
+	g.Connect(BasicEdge(5, 6))
+	g.Connect(BasicEdge(5, 7))
+	g.Connect(BasicEdge(5, 8))
+	g.Connect(BasicEdge(6, 7))
+	g.Connect(BasicEdge(6, 8))
+	g.Connect(BasicEdge(7, 8))
+	g.TransitiveReduction()
+
+	actual := strings.TrimSpace(g.String())
+	expected := strings.TrimSpace(testGraphTransReductionMultipleRootsStr)
+	if actual != expected {
+		t.Fatalf("bad: %s", actual)
+	}
+}
+
 // use this to simulate slow sort operations
 type counter struct {
 	Name  string
@@ -429,3 +461,20 @@ const testGraphTransReductionMoreStr = `
   4
 4
 `
+
+const testGraphTransReductionMultipleRootsStr = `
+1
+  2
+2
+  3
+3
+  4
+4
+5
+  6
+6
+  7
+7
+  8
+8
+`