diff --git a/gg/gg.go b/gg/gg.go
index 2ba705d..64db16d 100644
--- a/gg/gg.go
+++ b/gg/gg.go
@@ -437,3 +437,43 @@ func Equal(g1, g2 *Graph) bool {
 	}
 	return true
 }
+
+// Walk will traverse the Graph, calling the callback on every Vertex in the
+// Graph once. If startWith is non-nil then that Vertex will be the first one
+// passed to the callback and used as the starting point of the traversal. If
+// the callback returns false the traversal is stopped.
+func (g *Graph) Walk(startWith *Vertex, callback func(*Vertex) bool) {
+	g.makeView()
+	if len(g.view) == 0 {
+		return
+	}
+
+	seen := make(map[*Vertex]bool, len(g.view))
+	var innerWalk func(*Vertex) bool
+	innerWalk = func(v *Vertex) bool {
+		if seen[v] {
+			return true
+		} else if !callback(v) {
+			return false
+		}
+		seen[v] = true
+		for _, e := range v.In {
+			if !innerWalk(e.From) {
+				return false
+			}
+		}
+		return true
+	}
+
+	if startWith != nil {
+		if !innerWalk(startWith) {
+			return
+		}
+	}
+
+	for _, v := range g.view {
+		if !innerWalk(v) {
+			return
+		}
+	}
+}
diff --git a/gg/gg_test.go b/gg/gg_test.go
index 8ca7012..d226bd1 100644
--- a/gg/gg_test.go
+++ b/gg/gg_test.go
@@ -68,14 +68,37 @@ func assertVertexEqual(t *T, exp, got *Vertex, msgAndArgs ...interface{}) bool {
 	return assertInner(exp, got, map[*Vertex]bool{})
 }
 
-type graphTest struct {
-	name string
-	out  func() *Graph
-	exp  []*Vertex
+func assertWalk(t *T, expVals, expJuncs int, g *Graph, msgAndArgs ...interface{}) {
+	seen := map[*Vertex]bool{}
+	var gotVals, gotJuncs int
+	g.Walk(nil, func(v *Vertex) bool {
+		assert.NotContains(t, seen, v, msgAndArgs...)
+		seen[v] = true
+		if v.VertexType == Value {
+			gotVals++
+		} else {
+			gotJuncs++
+		}
+		return true
+	})
+	assert.Equal(t, expVals, gotVals, msgAndArgs...)
+	assert.Equal(t, expJuncs, gotJuncs, msgAndArgs...)
 }
 
-func mkTest(name string, out func() *Graph, exp ...*Vertex) graphTest {
-	return graphTest{name: name, out: out, exp: exp}
+type graphTest struct {
+	name              string
+	out               func() *Graph
+	exp               []*Vertex
+	numVals, numJuncs int
+}
+
+func mkTest(name string, out func() *Graph, numVals, numJuncs int, exp ...*Vertex) graphTest {
+	return graphTest{
+		name:    name,
+		out:     out,
+		exp:     exp,
+		numVals: numVals, numJuncs: numJuncs,
+	}
 }
 
 func TestGraph(t *T) {
@@ -85,6 +108,7 @@ func TestGraph(t *T) {
 			func() *Graph {
 				return Null.AddValueIn(ValueOut(id("v0"), id("e0")), id("v1"))
 			},
+			2, 0,
 			value("v0"),
 			value("v1", edge("e0", value("v0"))),
 		),
@@ -95,6 +119,7 @@ func TestGraph(t *T) {
 				g0 := Null.AddValueIn(ValueOut(id("v0"), id("e0")), id("v2"))
 				return g0.AddValueIn(ValueOut(id("v1"), id("e1")), id("v2"))
 			},
+			3, 0,
 			value("v0"),
 			value("v1"),
 			value("v2",
@@ -109,6 +134,7 @@ func TestGraph(t *T) {
 				g0 := Null.AddValueIn(ValueOut(id("v0"), id("e0")), id("v1"))
 				return g0.AddValueIn(ValueOut(id("v2"), id("e2")), id("v3"))
 			},
+			4, 0,
 			value("v0"),
 			value("v1", edge("e0", value("v0"))),
 			value("v2"),
@@ -120,6 +146,7 @@ func TestGraph(t *T) {
 			func() *Graph {
 				return Null.AddValueIn(ValueOut(id("v0"), id("e")), id("v0"))
 			},
+			1, 0,
 			value("v0", edge("e", value("v0"))),
 		),
 
@@ -129,6 +156,7 @@ func TestGraph(t *T) {
 				g0 := Null.AddValueIn(ValueOut(id("v0"), id("e0")), id("v1"))
 				return g0.AddValueIn(ValueOut(id("v1"), id("e1")), id("v0"))
 			},
+			2, 0,
 			value("v0", edge("e1", value("v1", edge("e0", value("v0"))))),
 			value("v1", edge("e0", value("v0", edge("e1", value("v1"))))),
 		),
@@ -140,6 +168,7 @@ func TestGraph(t *T) {
 				g1 := g0.AddValueIn(ValueOut(id("v1"), id("e1")), id("v2"))
 				return g1.AddValueIn(ValueOut(id("v2"), id("e2")), id("v1"))
 			},
+			3, 0,
 			value("v0"),
 			value("v1",
 				edge("e0", value("v0")),
@@ -159,6 +188,7 @@ func TestGraph(t *T) {
 				ej0 := JunctionOut([]OpenEdge{e0, e1}, id("ej0"))
 				return Null.AddValueIn(ej0, id("v2"))
 			},
+			3, 1,
 			value("v0"), value("v1"),
 			value("v2", junction("ej0",
 				edge("e0", value("v0")),
@@ -178,6 +208,7 @@ func TestGraph(t *T) {
 				ej2 := JunctionOut([]OpenEdge{ej0, ej1}, id("ej2"))
 				return Null.AddValueIn(ej2, id("v2"))
 			},
+			3, 3,
 			value("v0"), value("v1"),
 			value("v2", junction("ej2",
 				junction("ej0",
@@ -203,6 +234,7 @@ func TestGraph(t *T) {
 				e21 := ValueOut(id("v2"), id("e21"))
 				return g1.AddValueIn(e21, id("v1"))
 			},
+			3, 1,
 			value("v0", edge("e20", value("v2", junction("ej0",
 				edge("e0", value("v0")),
 				edge("e1", value("v1", edge("e21", value("v2")))),
@@ -219,6 +251,7 @@ func TestGraph(t *T) {
 	}
 
 	for i := range tests {
+		t.Logf("test[%d]:%q", i, tests[i].name)
 		out := tests[i].out()
 		for j, exp := range tests[i].exp {
 			msgAndArgs := []interface{}{
@@ -232,8 +265,16 @@ func TestGraph(t *T) {
 			assertVertexEqual(t, exp, v, msgAndArgs...)
 		}
 
+		msgAndArgs := []interface{}{
+			"tests[%d].name:%q",
+			i, tests[i].name,
+		}
+
 		// sanity check that graphs are equal to themselves
-		assert.True(t, Equal(out, out))
+		assert.True(t, Equal(out, out), msgAndArgs...)
+
+		// test the Walk method in here too
+		assertWalk(t, tests[i].numVals, tests[i].numJuncs, out, msgAndArgs...)
 	}
 }