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