def test_min_maximal_matching_bqm(self):
bqm = dnx.min_maximal_matching_bqm(self.graph)
if len(self.graph) == 0:
self.assertEqual(len(bqm.linear), 0)
return
# the ground states should be exactly the minimum maximal matchings of
# G
sampleset = dimod.ExactSolver().sample(bqm)
# we'd like to use sampleset.lowest() but it didn't exist in dimod
# 0.8.0
ground_energy = sampleset.first.energy
cardinalities = set()
for sample, energy in sampleset.data(['sample', 'energy']):
if energy > ground_energy:
continue
edges = set(v for v, val in sample.items() if val > 0)
self.assertTrue(nx.is_maximal_matching(self.graph, edges))
cardinalities.add(len(edges))
# all ground have the same cardinality (or it's empty)
self.assertEqual(len(cardinalities), 1)
cardinality, = cardinalities
# everything that's not ground has a higher energy
for sample, energy in sampleset.data(['sample', 'energy']):
edges = set(v for v, val in sample.items() if val > 0)
if energy != sampleset.first.energy:
if nx.is_maximal_matching(self.graph, edges):
self.assertGreater(len(edges), cardinality)
def test_maximal_matching_bqm(self):
bqm = dnx.maximal_matching_bqm(self.graph)
# the ground states should be exactly the maximal matchings of G
sampleset = dimod.ExactSolver().sample(bqm)
for sample, energy in sampleset.data(['sample', 'energy']):
edges = set(v for v, val in sample.items() if val > 0)
self.assertEqual(nx.is_maximal_matching(self.graph, edges),
energy == 0)
self.assertGreaterEqual(energy, 0)
# while we're at it, test deprecated is_maximal_matching
with self.assertWarns(DeprecationWarning):
self.assertEqual(nx.is_maximal_matching(self.graph, edges),
dnx.is_maximal_matching(self.graph, edges))
def test_self_loops(self):
# Create the path graph with two self-loops.
G = nx.path_graph(3)
G.add_edges_from([(0, 0), (1, 1)])
matching = nx.maximal_matching(G)
assert_equal(len(matching), 1)
# The matching should never include self-loops.
assert_false(any(u == v for u, v in matching))
assert_true(nx.is_maximal_matching(G, matching))
def test_self_loops(self):
# Create the path graph with two self-loops.
G = nx.path_graph(3)
G.add_edges_from([(0, 0), (1, 1)])
matching = nx.maximal_matching(G)
assert_equal(len(matching), 1)
# The matching should never include self-loops.
assert_false(any(u == v for u, v in matching))
assert_true(nx.is_maximal_matching(G, matching))
def test_ordering(self):
"""Tests that a maximal matching is computed correctly
regardless of the order in which nodes are added to the graph.
"""
for nodes in permutations(range(3)):
G = nx.Graph()
G.add_nodes_from(nodes)
G.add_edges_from([(0, 1), (0, 2)])
matching = nx.maximal_matching(G)
assert_equal(len(matching), 1)
assert_true(nx.is_maximal_matching(G, matching))
def test_ordering(self):
"""Tests that a maximal matching is computed correctly
regardless of the order in which nodes are added to the graph.
"""
for nodes in permutations(range(3)):
G = nx.Graph()
G.add_nodes_from(nodes)
G.add_edges_from([(0, 1), (0, 2)])
matching = nx.maximal_matching(G)
assert_equal(len(matching), 1)
assert_true(nx.is_maximal_matching(G, matching))
def test_not_matching(self):
G = nx.path_graph(4)
assert_false(nx.is_maximal_matching(G, set([(0, 1), (1, 2), (2, 3)])))
def test_single_edge_matching(self):
# In the star graph, any maximal matching has just one edge.
G = nx.star_graph(5)
matching = nx.maximal_matching(G)
assert_equal(1, len(matching))
assert_true(nx.is_maximal_matching(G, matching))
def test_dict(self):
G = nx.path_graph(4)
assert_true(nx.is_maximal_matching(G, {0: 1, 1: 0, 2: 3, 3: 2}))
def test_not_maximal(self):
G = nx.path_graph(4)
assert_false(nx.is_maximal_matching(G, {(0, 1)}))
def test_valid_matching(self):
edges = [(1, 2), (1, 5), (2, 3), (2, 5), (3, 4), (3, 6), (5, 6)]
G = nx.Graph(edges)
matching = nx.maximal_matching(G)
assert_true(nx.is_maximal_matching(G, matching))
def test_dict(self):
G = nx.path_graph(4)
assert_true(nx.is_maximal_matching(G, {0: 1, 1: 0, 2: 3, 3: 2}))
def test_valid(self):
G = nx.path_graph(4)
assert_true(nx.is_maximal_matching(G, {(0, 1), (2, 3)}))
def is_matching(self, plays):
"""
check if the pulled edges form a matching in the given bipartite graph
"""
match = self.plays_to_edges(plays)
return nx.is_maximal_matching(self.graph, match) # TODO
def test_not_matching(self):
G = nx.path_graph(4)
assert not nx.is_maximal_matching(G, {(0, 1), (1, 2), (2, 3)})
def test_min_maximal_matching(self):
matching = dnx.min_maximal_matching(self.graph, dimod.ExactSolver())
self.assertTrue(nx.is_maximal_matching(self.graph, matching))
def test_single_edge_matching(self):
# In the star graph, any maximal matching has just one edge.
G = nx.star_graph(5)
matching = nx.maximal_matching(G)
assert_equal(1, len(matching))
assert_true(nx.is_maximal_matching(G, matching))
def test_valid_matching(self):
edges = [(1, 2), (1, 5), (2, 3), (2, 5), (3, 4), (3, 6), (5, 6)]
G = nx.Graph(edges)
matching = nx.maximal_matching(G)
assert_true(nx.is_maximal_matching(G, matching))
def test_not_maximal(self):
G = nx.path_graph(4)
assert_false(nx.is_maximal_matching(G, {(0, 1)}))
def test_valid(self):
G = nx.path_graph(4)
assert_true(nx.is_maximal_matching(G, {(0, 1), (2, 3)}))
