diff --git a/skimage/graph/graph_cut.py b/skimage/graph/graph_cut.py
index 3f973e22..d7710f0b 100644
--- a/skimage/graph/graph_cut.py
+++ b/skimage/graph/graph_cut.py
@@ -72,7 +72,8 @@ def cut_threshold(labels, rag, thresh, in_place=True):
     return map_array[labels]
 
 
-def cut_normalized(labels, rag, thresh=0.001, num_cuts=10, in_place=True):
+def cut_normalized(labels, rag, thresh=0.001, num_cuts=10, in_place=True,
+                   max_edge=1.0):
     """Perform Normalized Graph cut on the Region Adjacency Graph.
 
     Given an image's labels and its similarity RAG, recursively perform
@@ -94,6 +95,10 @@ def cut_normalized(labels, rag, thresh=0.001, num_cuts=10, in_place=True):
     in_place : bool
         If set, modifies `rag` in place. For each node `n` the function will
         set a new attribute ``rag.node[n]['ncut label']``.
+    max_edge : float, optional
+        The maximum possible value of an edge in the RAG. This corresponds to
+        an edge between identical regions. This is used to put self
+        edges in the RAG.
 
     Returns
     -------
@@ -118,6 +123,9 @@ def cut_normalized(labels, rag, thresh=0.001, num_cuts=10, in_place=True):
     if not in_place:
         rag = rag.copy()
 
+    for node in rag.nodes_iter():
+        rag.add_edge(node, node, weight=max_edge)
+
     _ncut_relabel(rag, thresh, num_cuts)
 
     map_array = np.zeros(labels.max() + 1)
diff --git a/skimage/graph/rag.py b/skimage/graph/rag.py
index 5ef9a83b..df9b4ebf 100644
--- a/skimage/graph/rag.py
+++ b/skimage/graph/rag.py
@@ -115,7 +115,8 @@ def _add_edge_filter(values, graph):
     values = values.astype(int)
     current = values[0]
     for value in values[1:]:
-        graph.add_edge(current, value)
+        if value != current:
+            graph.add_edge(current, value)
 
     return 0
 
diff --git a/skimage/graph/tests/test_rag.py b/skimage/graph/tests/test_rag.py
index 0e62aa1a..26f5a85c 100644
--- a/skimage/graph/tests/test_rag.py
+++ b/skimage/graph/tests/test_rag.py
@@ -104,5 +104,7 @@ def test_cut_normalized():
 def test_rag_error():
     img = np.zeros((10, 10, 3), dtype='uint8')
     labels = np.zeros((10, 10), dtype='uint8')
+    labels[:5, :] = 0
+    labels[5:, :] = 1
     testing.assert_raises(ValueError, graph.rag_mean_color, img, labels,
                           2, 'non existant mode')