I think I have a smaller example:

sage: G = Graph([(0, 3, 1), (0, 4, 1), (1, 2, 1), (2, 3, 1), (2, 4, 1)])
sage: G.edge_cut(0,1,value_only=False,use_edge_labels=True)
[1, [(0, 3, 1), (1, 2, 1), (2, 3, 1)]]
sage: G.edge_cut(0,1,value_only=False,use_edge_labels=True,method='LP')
(1.0, [(1, 2)])

This should make debugging easier.


Doug

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