diff --git a/.gitignore b/.gitignore
index fbaf40d11fa..1ee2944de32 100644
--- a/.gitignore
+++ b/.gitignore
@@ -21,5 +21,5 @@ doc/source/examples/*
 
 # Generated when 'python setup_egg.py'
 networkx.egg-info/
-Networkx.sublime-project
-Networkx.sublime-workspace
+*.sublime-project
+*.sublime-workspace
diff --git a/networkx/classes/function.py b/networkx/classes/function.py
index 321d8be59a9..9f035b9848f 100644
--- a/networkx/classes/function.py
+++ b/networkx/classes/function.py
@@ -18,7 +18,7 @@
            'freeze','is_frozen','subgraph','create_empty_copy',
            'set_node_attributes','get_node_attributes',
            'set_edge_attributes','get_edge_attributes',
-           'all_neighbors','non_neighbors']
+           'all_neighbors','non_neighbors', 'non_edges']
 
 def nodes(G):
     """Return a copy of the graph nodes in a list."""
@@ -425,3 +425,28 @@ def non_neighbors(graph, node):
     """
     nbors = set(neighbors(graph, node)) | set([node])
     return (nnode for nnode in graph if nnode not in nbors)
+
+def non_edges(graph):
+    """Returns the non-existent edges in the graph.
+
+    Parameters
+    ----------
+    graph : NetworkX graph.
+        Graph to find non-existent edges.
+
+    Returns
+    -------
+    non_edges : iterator
+        Iterator of edges that are not in the graph.
+    """
+    if graph.is_directed():
+        for u in graph.nodes_iter():
+            for v in non_neighbors(graph, u):
+                yield (u, v)
+    else:
+        S = set()
+        for u in graph.nodes_iter():
+            for v in non_neighbors(graph, u):
+                if (u, v) not in S:
+                    yield (u, v)
+                    S.add((v, u))
diff --git a/networkx/classes/tests/test_function.py b/networkx/classes/tests/test_function.py
index 2c121787772..f813908ac20 100644
--- a/networkx/classes/tests/test_function.py
+++ b/networkx/classes/tests/test_function.py
@@ -188,3 +188,29 @@ def test_non_neighbors(self):
         graph.add_nodes_from(range(10))
         nbors = list(nx.non_neighbors(graph, 0))
         assert_equal(len(nbors), 9)
+
+    def test_non_edges(self):
+        # All possible edges exist
+        graph = nx.complete_graph(5)
+        nedges = list(nx.non_edges(graph))
+        assert len(nedges) == 0
+
+        graph = nx.path_graph(4)
+        expected = [(0, 2), (0, 3), (1, 3)]
+        nedges = list(nx.non_edges(graph))
+        for (u, v) in expected:
+            assert (u, v) in nedges or (v, u) in nedges
+
+        graph = nx.star_graph(4)
+        expected = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
+        nedges = list(nx.non_edges(graph))
+        for (u, v) in expected:
+            assert (u, v) in nedges or (v, u) in nedges
+
+        # Directed graphs
+        graph = nx.DiGraph()
+        graph.add_edges_from([(0, 2), (2, 0), (2, 1)])
+        expected = [(0, 1), (1, 0), (1, 2)]
+        nedges = list(nx.non_edges(graph))
+        for e in expected:
+            assert e in nedges