355 lines
14 KiB
Python
355 lines
14 KiB
Python
from itertools import permutations
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import math
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import networkx as nx
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from networkx.algorithms.matching import matching_dict_to_set
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from networkx.testing import assert_edges_equal
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class TestMaxWeightMatching(object):
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"""Unit tests for the
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:func:`~networkx.algorithms.matching.max_weight_matching` function.
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"""
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def test_trivial1(self):
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"""Empty graph"""
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G = nx.Graph()
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assert nx.max_weight_matching(G) == set()
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def test_trivial2(self):
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"""Self loop"""
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G = nx.Graph()
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G.add_edge(0, 0, weight=100)
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assert nx.max_weight_matching(G) == set()
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def test_trivial3(self):
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"""Single edge"""
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G = nx.Graph()
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G.add_edge(0, 1)
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assert_edges_equal(nx.max_weight_matching(G),
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matching_dict_to_set({0: 1, 1: 0}))
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def test_trivial4(self):
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"""Small graph"""
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G = nx.Graph()
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G.add_edge('one', 'two', weight=10)
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G.add_edge('two', 'three', weight=11)
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assert_edges_equal(nx.max_weight_matching(G),
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matching_dict_to_set({'three': 'two', 'two': 'three'}))
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def test_trivial5(self):
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"""Path"""
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G = nx.Graph()
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G.add_edge(1, 2, weight=5)
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G.add_edge(2, 3, weight=11)
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G.add_edge(3, 4, weight=5)
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assert_edges_equal(nx.max_weight_matching(G),
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matching_dict_to_set({2: 3, 3: 2}))
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assert_edges_equal(nx.max_weight_matching(G, 1),
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matching_dict_to_set({1: 2, 2: 1, 3: 4, 4: 3}))
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def test_trivial6(self):
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"""Small graph with arbitrary weight attribute"""
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G = nx.Graph()
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G.add_edge('one', 'two', weight=10, abcd=11)
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G.add_edge('two', 'three', weight=11, abcd=10)
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assert_edges_equal(nx.max_weight_matching(G, weight='abcd'),
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matching_dict_to_set({'one': 'two', 'two': 'one'}))
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def test_floating_point_weights(self):
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"""Floating point weights"""
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G = nx.Graph()
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G.add_edge(1, 2, weight=math.pi)
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G.add_edge(2, 3, weight=math.exp(1))
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G.add_edge(1, 3, weight=3.0)
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G.add_edge(1, 4, weight=math.sqrt(2.0))
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assert_edges_equal(nx.max_weight_matching(G),
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matching_dict_to_set({1: 4, 2: 3, 3: 2, 4: 1}))
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def test_negative_weights(self):
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"""Negative weights"""
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G = nx.Graph()
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G.add_edge(1, 2, weight=2)
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G.add_edge(1, 3, weight=-2)
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G.add_edge(2, 3, weight=1)
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G.add_edge(2, 4, weight=-1)
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G.add_edge(3, 4, weight=-6)
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assert_edges_equal(nx.max_weight_matching(G),
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matching_dict_to_set({1: 2, 2: 1}))
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assert_edges_equal(nx.max_weight_matching(G, 1),
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matching_dict_to_set({1: 3, 2: 4, 3: 1, 4: 2}))
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def test_s_blossom(self):
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"""Create S-blossom and use it for augmentation:"""
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G = nx.Graph()
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G.add_weighted_edges_from([(1, 2, 8), (1, 3, 9),
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(2, 3, 10), (3, 4, 7)])
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assert_edges_equal(nx.max_weight_matching(G),
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matching_dict_to_set({1: 2, 2: 1, 3: 4, 4: 3}))
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G.add_weighted_edges_from([(1, 6, 5), (4, 5, 6)])
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assert_edges_equal(nx.max_weight_matching(G),
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matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 5, 5: 4, 6: 1}))
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def test_s_t_blossom(self):
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"""Create S-blossom, relabel as T-blossom, use for augmentation:"""
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G = nx.Graph()
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G.add_weighted_edges_from([(1, 2, 9), (1, 3, 8), (2, 3, 10),
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(1, 4, 5), (4, 5, 4), (1, 6, 3)])
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assert_edges_equal(nx.max_weight_matching(G),
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matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 5, 5: 4, 6: 1}))
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G.add_edge(4, 5, weight=3)
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G.add_edge(1, 6, weight=4)
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assert_edges_equal(nx.max_weight_matching(G),
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matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 5, 5: 4, 6: 1}))
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G.remove_edge(1, 6)
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G.add_edge(3, 6, weight=4)
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assert_edges_equal(nx.max_weight_matching(G),
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matching_dict_to_set({1: 2, 2: 1, 3: 6, 4: 5, 5: 4, 6: 3}))
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def test_nested_s_blossom(self):
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"""Create nested S-blossom, use for augmentation:"""
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G = nx.Graph()
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G.add_weighted_edges_from([(1, 2, 9), (1, 3, 9), (2, 3, 10),
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(2, 4, 8), (3, 5, 8), (4, 5, 10),
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(5, 6, 6)])
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dict_format = {1: 3, 2: 4, 3: 1, 4: 2, 5: 6, 6: 5}
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expected = {frozenset(e) for e in matching_dict_to_set(dict_format)}
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answer = {frozenset(e) for e in nx.max_weight_matching(G)}
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assert answer == expected
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def test_nested_s_blossom_relabel(self):
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"""Create S-blossom, relabel as S, include in nested S-blossom:"""
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G = nx.Graph()
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G.add_weighted_edges_from([(1, 2, 10), (1, 7, 10), (2, 3, 12),
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(3, 4, 20), (3, 5, 20), (4, 5, 25),
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(5, 6, 10), (6, 7, 10), (7, 8, 8)])
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assert_edges_equal(nx.max_weight_matching(G),
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matching_dict_to_set({1: 2, 2: 1, 3: 4, 4: 3, 5: 6, 6: 5, 7: 8, 8: 7}))
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def test_nested_s_blossom_expand(self):
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"""Create nested S-blossom, augment, expand recursively:"""
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G = nx.Graph()
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G.add_weighted_edges_from([(1, 2, 8), (1, 3, 8), (2, 3, 10),
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(2, 4, 12), (3, 5, 12), (4, 5, 14),
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(4, 6, 12), (5, 7, 12), (6, 7, 14),
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(7, 8, 12)])
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assert_edges_equal(nx.max_weight_matching(G),
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matching_dict_to_set({1: 2, 2: 1, 3: 5, 4: 6, 5: 3, 6: 4, 7: 8, 8: 7}))
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def test_s_blossom_relabel_expand(self):
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"""Create S-blossom, relabel as T, expand:"""
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G = nx.Graph()
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G.add_weighted_edges_from([(1, 2, 23), (1, 5, 22), (1, 6, 15),
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(2, 3, 25), (3, 4, 22), (4, 5, 25),
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(4, 8, 14), (5, 7, 13)])
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assert_edges_equal(nx.max_weight_matching(G),
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matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 8, 5: 7, 6: 1, 7: 5, 8: 4}))
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def test_nested_s_blossom_relabel_expand(self):
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"""Create nested S-blossom, relabel as T, expand:"""
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G = nx.Graph()
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G.add_weighted_edges_from([(1, 2, 19), (1, 3, 20), (1, 8, 8),
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(2, 3, 25), (2, 4, 18), (3, 5, 18),
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(4, 5, 13), (4, 7, 7), (5, 6, 7)])
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assert_edges_equal(nx.max_weight_matching(G),
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matching_dict_to_set({1: 8, 2: 3, 3: 2, 4: 7, 5: 6, 6: 5, 7: 4, 8: 1}))
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def test_nasty_blossom1(self):
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"""Create blossom, relabel as T in more than one way, expand,
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augment:
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"""
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G = nx.Graph()
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G.add_weighted_edges_from([(1, 2, 45), (1, 5, 45), (2, 3, 50),
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(3, 4, 45), (4, 5, 50), (1, 6, 30),
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(3, 9, 35), (4, 8, 35), (5, 7, 26),
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(9, 10, 5)])
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assert_edges_equal(nx.max_weight_matching(G),
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matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 8, 5: 7,
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6: 1, 7: 5, 8: 4, 9: 10, 10: 9}))
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def test_nasty_blossom2(self):
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"""Again but slightly different:"""
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G = nx.Graph()
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G.add_weighted_edges_from([(1, 2, 45), (1, 5, 45), (2, 3, 50),
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(3, 4, 45), (4, 5, 50), (1, 6, 30),
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(3, 9, 35), (4, 8, 26), (5, 7, 40),
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(9, 10, 5)])
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assert_edges_equal(nx.max_weight_matching(G),
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matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 8, 5: 7,
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6: 1, 7: 5, 8: 4, 9: 10, 10: 9}))
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def test_nasty_blossom_least_slack(self):
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"""Create blossom, relabel as T, expand such that a new
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least-slack S-to-free dge is produced, augment:
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"""
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G = nx.Graph()
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G.add_weighted_edges_from([(1, 2, 45), (1, 5, 45), (2, 3, 50),
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(3, 4, 45), (4, 5, 50), (1, 6, 30),
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(3, 9, 35), (4, 8, 28), (5, 7, 26),
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(9, 10, 5)])
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assert_edges_equal(nx.max_weight_matching(G),
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matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 8, 5: 7,
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6: 1, 7: 5, 8: 4, 9: 10, 10: 9}))
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def test_nasty_blossom_augmenting(self):
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"""Create nested blossom, relabel as T in more than one way"""
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# expand outer blossom such that inner blossom ends up on an
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# augmenting path:
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G = nx.Graph()
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G.add_weighted_edges_from([(1, 2, 45), (1, 7, 45), (2, 3, 50),
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(3, 4, 45), (4, 5, 95), (4, 6, 94),
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(5, 6, 94), (6, 7, 50), (1, 8, 30),
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(3, 11, 35), (5, 9, 36), (7, 10, 26),
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(11, 12, 5)])
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assert_edges_equal(nx.max_weight_matching(G),
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matching_dict_to_set({1: 8, 2: 3, 3: 2, 4: 6, 5: 9, 6: 4,
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7: 10, 8: 1, 9: 5, 10: 7, 11: 12, 12: 11}))
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def test_nasty_blossom_expand_recursively(self):
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"""Create nested S-blossom, relabel as S, expand recursively:"""
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G = nx.Graph()
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G.add_weighted_edges_from([(1, 2, 40), (1, 3, 40), (2, 3, 60),
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(2, 4, 55), (3, 5, 55), (4, 5, 50),
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(1, 8, 15), (5, 7, 30), (7, 6, 10),
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(8, 10, 10), (4, 9, 30)])
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assert_edges_equal(nx.max_weight_matching(G),
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matching_dict_to_set({1: 2, 2: 1, 3: 5, 4: 9, 5: 3,
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6: 7, 7: 6, 8: 10, 9: 4, 10: 8}))
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class TestIsMatching(object):
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"""Unit tests for the
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:func:`~networkx.algorithms.matching.is_matching` function.
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"""
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def test_dict(self):
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G = nx.path_graph(4)
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assert nx.is_matching(G, {0: 1, 1: 0, 2: 3, 3: 2})
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def test_empty_matching(self):
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G = nx.path_graph(4)
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assert nx.is_matching(G, set())
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def test_single_edge(self):
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G = nx.path_graph(4)
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assert nx.is_matching(G, {(1, 2)})
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def test_edge_order(self):
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G = nx.path_graph(4)
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assert nx.is_matching(G, {(0, 1), (2, 3)})
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assert nx.is_matching(G, {(1, 0), (2, 3)})
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assert nx.is_matching(G, {(0, 1), (3, 2)})
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assert nx.is_matching(G, {(1, 0), (3, 2)})
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def test_valid(self):
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G = nx.path_graph(4)
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assert nx.is_matching(G, {(0, 1), (2, 3)})
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def test_invalid(self):
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G = nx.path_graph(4)
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assert not nx.is_matching(G, {(0, 1), (1, 2), (2, 3)})
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class TestIsMaximalMatching(object):
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"""Unit tests for the
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:func:`~networkx.algorithms.matching.is_maximal_matching` function.
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"""
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def test_dict(self):
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G = nx.path_graph(4)
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assert nx.is_maximal_matching(G, {0: 1, 1: 0, 2: 3, 3: 2})
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def test_valid(self):
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G = nx.path_graph(4)
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assert nx.is_maximal_matching(G, {(0, 1), (2, 3)})
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def test_not_matching(self):
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G = nx.path_graph(4)
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assert not nx.is_maximal_matching(G, {(0, 1), (1, 2), (2, 3)})
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def test_not_maximal(self):
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G = nx.path_graph(4)
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assert not nx.is_maximal_matching(G, {(0, 1)})
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class TestIsPerfectMatching(object):
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"""Unit tests for the
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:func:`~networkx.algorithms.matching.is_perfect_matching` function.
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"""
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def test_dict(self):
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G = nx.path_graph(4)
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assert nx.is_perfect_matching(G, {0: 1, 1: 0, 2: 3, 3: 2})
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def test_valid(self):
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G = nx.path_graph(4)
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assert nx.is_perfect_matching(G, {(0, 1), (2, 3)})
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def test_valid_not_path(self):
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G = nx.cycle_graph(4)
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G.add_edge(0, 4)
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G.add_edge(1, 4)
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G.add_edge(5, 2)
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assert nx.is_perfect_matching(G, {(1, 4), (0, 3), (5, 2)})
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def test_not_matching(self):
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G = nx.path_graph(4)
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assert not nx.is_perfect_matching(G, {(0, 1), (1, 2), (2, 3)})
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def test_maximal_but_not_perfect(self):
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G = nx.cycle_graph(4)
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G.add_edge(0, 4)
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G.add_edge(1, 4)
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assert not nx.is_perfect_matching(G, {(1, 4), (0, 3)})
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class TestMaximalMatching(object):
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"""Unit tests for the
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:func:`~networkx.algorithms.matching.maximal_matching`.
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"""
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def test_valid_matching(self):
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edges = [(1, 2), (1, 5), (2, 3), (2, 5), (3, 4), (3, 6), (5, 6)]
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G = nx.Graph(edges)
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matching = nx.maximal_matching(G)
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assert nx.is_maximal_matching(G, matching)
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def test_single_edge_matching(self):
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# In the star graph, any maximal matching has just one edge.
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G = nx.star_graph(5)
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matching = nx.maximal_matching(G)
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assert 1 == len(matching)
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assert nx.is_maximal_matching(G, matching)
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def test_self_loops(self):
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# Create the path graph with two self-loops.
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G = nx.path_graph(3)
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G.add_edges_from([(0, 0), (1, 1)])
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matching = nx.maximal_matching(G)
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assert len(matching) == 1
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# The matching should never include self-loops.
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assert not any(u == v for u, v in matching)
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assert nx.is_maximal_matching(G, matching)
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def test_ordering(self):
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"""Tests that a maximal matching is computed correctly
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regardless of the order in which nodes are added to the graph.
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"""
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for nodes in permutations(range(3)):
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G = nx.Graph()
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G.add_nodes_from(nodes)
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G.add_edges_from([(0, 1), (0, 2)])
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matching = nx.maximal_matching(G)
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assert len(matching) == 1
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assert nx.is_maximal_matching(G, matching)
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