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import unittest
from igraph import Cut, Graph, EdgeSeq, InternalError
from itertools import combinations
from random import randint
class MaxFlowTests(unittest.TestCase):
def setUp(self):
self.g = Graph(4, [(0, 1), (0, 2), (1, 2), (1, 3), (2, 3)])
self.capacities = [4, 2, 10, 2, 2]
self.g.es["capacity"] = self.capacities
def testCapacities(self):
self.assertTrue(self.capacities == self.g.es.get_attribute_values("capacity"))
def testEdgeConnectivity(self):
self.assertTrue(self.g.edge_connectivity(0, 3) == 2)
self.assertTrue(Graph.Barabasi(50).edge_connectivity() == 1)
self.assertTrue(self.g.adhesion() == 2)
self.assertTrue(Graph.Tree(10, 3).adhesion() == 1)
self.assertTrue(Graph.Tree(10, 3, "out").adhesion() == 0)
self.assertRaises(ValueError, self.g.edge_connectivity, 0)
def testVertexConnectivity(self):
self.assertTrue(self.g.vertex_connectivity(0, 3) == 2)
self.assertTrue(Graph.Barabasi(50).vertex_connectivity() == 1)
self.assertTrue(self.g.cohesion() == 2)
self.assertTrue(Graph.Tree(10, 3).cohesion() == 1)
self.assertTrue(Graph.Tree(10, 3, "out").cohesion() == 0)
self.assertRaises(ValueError, self.g.vertex_connectivity, 0)
self.assertRaises(InternalError, self.g.vertex_connectivity, 0, 1)
self.assertTrue(self.g.vertex_connectivity(0, 1, neighbors="nodes") == 4)
self.assertTrue(self.g.vertex_connectivity(0, 1, neighbors="negative") == -1)
def testMaxFlowValue(self):
self.assertTrue(self.g.maxflow_value(0, 3) == 2)
self.assertTrue(self.g.maxflow_value(0, 3, self.capacities) == 4)
self.assertTrue(self.g.maxflow_value(0, 3, "capacity") == 4)
self.assertRaises(KeyError, self.g.maxflow_value, 0, 3, "unknown")
def testMaxFlow(self):
flow = self.g.maxflow(0, 3)
self.assertEqual(flow.value, 2)
self.assertEqual(flow.flow, [1, 1, 0, 1, 1])
flow = self.g.maxflow(0, 3, "capacity")
self.assertEqual(flow.value, 4)
self.assertEqual(flow.cut, [3, 4])
self.assertEqual([e.index for e in flow.es], [3, 4])
self.assertTrue(
set(flow.partition[0]).union(flow.partition[1])
== set(range(self.g.vcount()))
)
self.assertRaises(KeyError, self.g.maxflow, 0, 3, "unknown")
class CutTests(unittest.TestCase):
def constructSimpleGraph(self, directed=False):
g = Graph(4, [(0, 1), (0, 2), (1, 2), (1, 3), (2, 3)], directed)
g.es["capacity"] = [4, 2, 10, 2, 2]
return g
def constructLadderGraph(self, directed=False):
el = list(zip(list(range(0, 5)), list(range(1, 6))))
el += list(zip(list(range(6, 11)), list(range(7, 12))))
el += list(zip(list(range(0, 6)), list(range(6, 12))))
g = Graph(el, directed=directed)
return g
def testMinCutValue(self):
g = self.constructSimpleGraph()
self.assertTrue(g.mincut_value(0, 3) == 2)
self.assertTrue(g.mincut_value(0, 3, g.es["capacity"]) == 4)
self.assertTrue(g.mincut_value(0, 3, "capacity") == 4)
self.assertRaises(KeyError, g.mincut_value, 0, 3, "unknown")
self.assertTrue(g.mincut_value() == 2)
self.assertTrue(g.mincut_value(source=0) == 2)
self.assertTrue(g.mincut_value(target=2) == 2)
def testMinCut(self):
g = self.constructSimpleGraph()
mc = g.mincut()
self.assertTrue(isinstance(mc, Cut))
self.assertTrue(mc.value == 2)
self.assertTrue(
set(mc.partition[0]).union(mc.partition[1]) == set(range(g.vcount()))
)
self.assertTrue(isinstance(str(mc), str))
self.assertTrue(isinstance(repr(mc), str))
self.assertTrue(isinstance(mc.es, EdgeSeq))
self.assertTrue(len(mc.es) == 2)
mc = g.mincut(capacity="capacity")
self.assertTrue(mc.value == 4)
self.assertRaises(KeyError, g.mincut, capacity="unknown")
def testMinCutWithSourceAndTarget(self):
g = self.constructSimpleGraph()
mc = g.mincut(0, 3, "capacity")
self.assertTrue(isinstance(mc, Cut))
self.assertTrue(mc.cut == [3, 4])
self.assertTrue(mc.value == 4)
self.assertTrue(
set(mc.partition[0]).union(mc.partition[1]) == set(range(g.vcount()))
)
mc = g.mincut(0, 3)
self.assertTrue(isinstance(mc, Cut))
self.assertTrue(mc.cut == [3, 4])
self.assertTrue(mc.value == 2)
mc = g.mincut(2, 0, "capacity")
self.assertTrue(isinstance(mc, Cut))
self.assertTrue(mc.cut == [0, 1])
self.assertTrue(mc.value == 6)
self.assertRaises(ValueError, g.mincut, 2, capacity="capacity")
def testStMinCut(self):
g = self.constructSimpleGraph()
mc = g.st_mincut(0, 3, "capacity")
self.assertTrue(isinstance(mc, Cut))
self.assertTrue(mc.cut == [3, 4])
self.assertTrue(mc.value == 4)
self.assertTrue(
set(mc.partition[0]).union(mc.partition[1]) == set(range(g.vcount()))
)
mc = g.st_mincut(0, 3)
self.assertTrue(isinstance(mc, Cut))
self.assertTrue(mc.cut == [3, 4])
self.assertTrue(mc.value == 2)
mc = g.st_mincut(2, 0, "capacity")
self.assertTrue(isinstance(mc, Cut))
self.assertTrue(mc.cut == [0, 1])
self.assertTrue(mc.value == 6)
self.assertRaises(KeyError, g.st_mincut, 2, 0, capacity="unknown")
def testAllSTCuts1(self):
# Simple graph with four vertices
g = self.constructSimpleGraph(directed=True)
partitions = [
((0, 1, 1, 1), 2),
((0, 0, 1, 1), 3),
((0, 1, 0, 1), 2),
((0, 0, 0, 1), 2),
]
values = dict(partitions)
partitions = [partition for partition, _ in partitions]
for cut in g.all_st_cuts(0, 3):
membership = tuple(cut.membership)
self.assertTrue(
membership in partitions,
"%r not found among expected partitions" % (membership,),
)
self.assertEqual(cut.value, values[membership])
self.assertEqual(len(cut.es), values[membership])
partitions.remove(membership)
self.assertTrue(
partitions == [], "expected partitions not seen: %r" % (partitions,)
)
def testAllSTCuts2(self):
# "Ladder graph"
g = self.constructLadderGraph(directed=True)
cuts = g.all_st_cuts(0, 11)
self.assertEqual(len(cuts), 36)
self.assertEqual(len({tuple(cut.membership) for cut in cuts}), 36)
for cut in cuts:
g2 = g.copy()
g2.delete_edges(cut.es)
self.assertFalse(
g2.is_connected(), "%r is not a real cut" % (cut.membership,)
)
self.assertFalse(cut.value < 2 or cut.value > 6)
def testAllSTMinCuts2(self):
# "Ladder graph"
g = self.constructLadderGraph()
g.to_directed("mutual")
cuts = g.all_st_mincuts(0, 11)
self.assertEqual(len(cuts), 7)
self.assertEqual(len({tuple(cut.membership) for cut in cuts}), 7)
for cut in cuts:
self.assertEqual(cut.value, 2)
g2 = g.copy()
g2.delete_edges(cut.es)
self.assertFalse(
g2.is_connected(), "%r is not a real cut" % (cut.membership,)
)
g.es["capacity"] = [2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1]
cuts = g.all_st_mincuts(0, 11, "capacity")
self.assertEqual(len(cuts), 2)
self.assertEqual(cuts[0].membership, [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1])
self.assertEqual(cuts[1].membership, [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1])
self.assertEqual(cuts[0].value, 2)
self.assertEqual(cuts[1].value, 2)
class GomoryHuTests(unittest.TestCase):
def testEmpty(self):
g = Graph()
t = g.gomory_hu_tree()
self.assertEqual(0, t.vcount())
self.assertEqual(0, t.ecount())
def testSimpleExample(self):
g = Graph(
6,
[(0, 1), (0, 2), (1, 2), (1, 3), (1, 4), (2, 4), (3, 4), (3, 5), (4, 5)],
directed=False,
)
g.es["capacity"] = [1, 7, 1, 3, 2, 4, 1, 6, 2]
t = g.gomory_hu_tree("capacity")
self.validate_gomory_hu_tree(g, t)
def testDirected(self):
g = Graph(
6,
[(0, 1), (0, 2), (1, 2), (1, 3), (1, 4), (2, 4), (3, 4), (3, 5), (4, 5)],
directed=True,
)
g.es["capacity"] = [1, 7, 1, 3, 2, 4, 1, 6, 2]
self.assertRaises(InternalError, g.gomory_hu_tree, "capacity")
def testRandomGRG(self):
g = Graph.GRG(25, 0.4)
self.validate_gomory_hu_tree(g, g.gomory_hu_tree())
g.es["capacity"] = [randint(0, 10) for _ in range(g.ecount())]
self.validate_gomory_hu_tree(g, g.gomory_hu_tree("capacity"))
def validate_gomory_hu_tree(self, g, t):
n = g.vcount()
self.assertEqual(n, t.vcount())
self.assertEqual(n - 1, t.ecount())
self.assertFalse(t.is_directed())
if "capacity" in g.edge_attributes():
capacities = g.es["capacity"]
else:
capacities = None
for i, j in combinations(list(range(n)), 2):
path = t.get_shortest_paths(i, j, output="epath")
if path:
path = path[0]
expected_flow = min(t.es[path]["flow"])
observed_flow = g.maxflow_value(i, j, capacities)
self.assertEqual(observed_flow, expected_flow)
def suite():
flow_suite = unittest.defaultTestLoader.loadTestsFromTestCase(MaxFlowTests)
cut_suite = unittest.defaultTestLoader.loadTestsFromTestCase(CutTests)
gomory_hu_suite = unittest.defaultTestLoader.loadTestsFromTestCase(GomoryHuTests)
return unittest.TestSuite([flow_suite, cut_suite, gomory_hu_suite])
def test():
runner = unittest.TextTestRunner()
runner.run(suite())
if __name__ == "__main__":
test()
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