diff options
Diffstat (limited to '.venv/lib/python3.12/site-packages/networkx/algorithms/tests/test_matching.py')
| -rw-r--r-- | .venv/lib/python3.12/site-packages/networkx/algorithms/tests/test_matching.py | 605 |
1 files changed, 605 insertions, 0 deletions
diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/tests/test_matching.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/tests/test_matching.py new file mode 100644 index 00000000..37853e38 --- /dev/null +++ b/.venv/lib/python3.12/site-packages/networkx/algorithms/tests/test_matching.py @@ -0,0 +1,605 @@ +import math +from itertools import permutations + +from pytest import raises + +import networkx as nx +from networkx.algorithms.matching import matching_dict_to_set +from networkx.utils import edges_equal + + +class TestMaxWeightMatching: + """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() + assert nx.min_weight_matching(G) == set() + + def test_selfloop(self): + G = nx.Graph() + G.add_edge(0, 0, weight=100) + assert nx.max_weight_matching(G) == set() + assert nx.min_weight_matching(G) == set() + + def test_single_edge(self): + G = nx.Graph() + G.add_edge(0, 1) + assert edges_equal( + nx.max_weight_matching(G), matching_dict_to_set({0: 1, 1: 0}) + ) + assert edges_equal( + nx.min_weight_matching(G), matching_dict_to_set({0: 1, 1: 0}) + ) + + def test_two_path(self): + 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"}), + ) + assert edges_equal( + nx.min_weight_matching(G), + matching_dict_to_set({"one": "two", "two": "one"}), + ) + + def test_path(self): + 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}) + ) + assert edges_equal( + nx.min_weight_matching(G), matching_dict_to_set({1: 2, 3: 4}) + ) + assert edges_equal( + nx.min_weight_matching(G, 1), matching_dict_to_set({1: 2, 3: 4}) + ) + + def test_square(self): + G = nx.Graph() + G.add_edge(1, 4, weight=2) + G.add_edge(2, 3, weight=2) + G.add_edge(1, 2, weight=1) + G.add_edge(3, 4, weight=4) + assert edges_equal( + nx.max_weight_matching(G), matching_dict_to_set({1: 2, 3: 4}) + ) + assert edges_equal( + nx.min_weight_matching(G), matching_dict_to_set({1: 4, 2: 3}) + ) + + def test_edge_attribute_name(self): + 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"}), + ) + assert edges_equal( + nx.min_weight_matching(G, weight="abcd"), + matching_dict_to_set({"three": "two"}), + ) + + def test_floating_point_weights(self): + 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}) + ) + assert edges_equal( + nx.min_weight_matching(G), matching_dict_to_set({1: 4, 2: 3, 3: 2, 4: 1}) + ) + + def test_negative_weights(self): + 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, maxcardinality=True), + matching_dict_to_set({1: 3, 2: 4, 3: 1, 4: 2}), + ) + assert edges_equal( + nx.min_weight_matching(G), matching_dict_to_set({1: 2, 3: 4}) + ) + + 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)]) + answer = matching_dict_to_set({1: 2, 2: 1, 3: 4, 4: 3}) + assert edges_equal(nx.max_weight_matching(G), answer) + assert edges_equal(nx.min_weight_matching(G), answer) + + G.add_weighted_edges_from([(1, 6, 5), (4, 5, 6)]) + answer = matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 5, 5: 4, 6: 1}) + assert edges_equal(nx.max_weight_matching(G), answer) + assert edges_equal(nx.min_weight_matching(G), answer) + + 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)] + ) + answer = matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 5, 5: 4, 6: 1}) + assert edges_equal(nx.max_weight_matching(G), answer) + assert edges_equal(nx.min_weight_matching(G), answer) + + G.add_edge(4, 5, weight=3) + G.add_edge(1, 6, weight=4) + assert edges_equal(nx.max_weight_matching(G), answer) + assert edges_equal(nx.min_weight_matching(G), answer) + + G.remove_edge(1, 6) + G.add_edge(3, 6, weight=4) + answer = matching_dict_to_set({1: 2, 2: 1, 3: 6, 4: 5, 5: 4, 6: 3}) + assert edges_equal(nx.max_weight_matching(G), answer) + assert edges_equal(nx.min_weight_matching(G), answer) + + 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 + answer = {frozenset(e) for e in nx.min_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), + ] + ) + answer = matching_dict_to_set({1: 2, 2: 1, 3: 4, 4: 3, 5: 6, 6: 5, 7: 8, 8: 7}) + assert edges_equal(nx.max_weight_matching(G), answer) + assert edges_equal(nx.min_weight_matching(G), answer) + + 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), + ] + ) + answer = matching_dict_to_set({1: 2, 2: 1, 3: 5, 4: 6, 5: 3, 6: 4, 7: 8, 8: 7}) + assert edges_equal(nx.max_weight_matching(G), answer) + assert edges_equal(nx.min_weight_matching(G), answer) + + 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), + ] + ) + answer = matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 8, 5: 7, 6: 1, 7: 5, 8: 4}) + assert edges_equal(nx.max_weight_matching(G), answer) + assert edges_equal(nx.min_weight_matching(G), answer) + + 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), + ] + ) + answer = matching_dict_to_set({1: 8, 2: 3, 3: 2, 4: 7, 5: 6, 6: 5, 7: 4, 8: 1}) + assert edges_equal(nx.max_weight_matching(G), answer) + assert edges_equal(nx.min_weight_matching(G), answer) + + 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), + ] + ) + ansdict = {1: 6, 2: 3, 3: 2, 4: 8, 5: 7, 6: 1, 7: 5, 8: 4, 9: 10, 10: 9} + answer = matching_dict_to_set(ansdict) + assert edges_equal(nx.max_weight_matching(G), answer) + assert edges_equal(nx.min_weight_matching(G), answer) + + 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), + ] + ) + ans = {1: 6, 2: 3, 3: 2, 4: 8, 5: 7, 6: 1, 7: 5, 8: 4, 9: 10, 10: 9} + answer = matching_dict_to_set(ans) + assert edges_equal(nx.max_weight_matching(G), answer) + assert edges_equal(nx.min_weight_matching(G), answer) + + 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), + ] + ) + ans = {1: 6, 2: 3, 3: 2, 4: 8, 5: 7, 6: 1, 7: 5, 8: 4, 9: 10, 10: 9} + answer = matching_dict_to_set(ans) + assert edges_equal(nx.max_weight_matching(G), answer) + assert edges_equal(nx.min_weight_matching(G), answer) + + 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), + ] + ) + ans = { + 1: 8, + 2: 3, + 3: 2, + 4: 6, + 5: 9, + 6: 4, + 7: 10, + 8: 1, + 9: 5, + 10: 7, + 11: 12, + 12: 11, + } + answer = matching_dict_to_set(ans) + assert edges_equal(nx.max_weight_matching(G), answer) + assert edges_equal(nx.min_weight_matching(G), answer) + + 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), + ] + ) + ans = {1: 2, 2: 1, 3: 5, 4: 9, 5: 3, 6: 7, 7: 6, 8: 10, 9: 4, 10: 8} + answer = matching_dict_to_set(ans) + assert edges_equal(nx.max_weight_matching(G), answer) + assert edges_equal(nx.min_weight_matching(G), answer) + + def test_wrong_graph_type(self): + error = nx.NetworkXNotImplemented + raises(error, nx.max_weight_matching, nx.MultiGraph()) + raises(error, nx.max_weight_matching, nx.MultiDiGraph()) + raises(error, nx.max_weight_matching, nx.DiGraph()) + raises(error, nx.min_weight_matching, nx.DiGraph()) + + +class TestIsMatching: + """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_matching(self): + G = nx.path_graph(4) + assert nx.is_matching(G, {(0, 1), (2, 3)}) + + def test_invalid_input(self): + error = nx.NetworkXError + G = nx.path_graph(4) + # edge to node not in G + raises(error, nx.is_matching, G, {(0, 5), (2, 3)}) + # edge not a 2-tuple + raises(error, nx.is_matching, G, {(0, 1, 2), (2, 3)}) + raises(error, nx.is_matching, G, {(0,), (2, 3)}) + + def test_selfloops(self): + error = nx.NetworkXError + G = nx.path_graph(4) + # selfloop for node not in G + raises(error, nx.is_matching, G, {(5, 5), (2, 3)}) + # selfloop edge not in G + assert not nx.is_matching(G, {(0, 0), (1, 2), (2, 3)}) + # selfloop edge in G + G.add_edge(0, 0) + assert not nx.is_matching(G, {(0, 0), (1, 2)}) + + def test_invalid_matching(self): + G = nx.path_graph(4) + assert not nx.is_matching(G, {(0, 1), (1, 2), (2, 3)}) + + def test_invalid_edge(self): + G = nx.path_graph(4) + assert not nx.is_matching(G, {(0, 3), (1, 2)}) + raises(nx.NetworkXError, nx.is_matching, G, {(0, 55)}) + + G = nx.DiGraph(G.edges) + assert nx.is_matching(G, {(0, 1)}) + assert not nx.is_matching(G, {(1, 0)}) + + +class TestIsMaximalMatching: + """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_invalid_input(self): + error = nx.NetworkXError + G = nx.path_graph(4) + # edge to node not in G + raises(error, nx.is_maximal_matching, G, {(0, 5)}) + raises(error, nx.is_maximal_matching, G, {(5, 0)}) + # edge not a 2-tuple + raises(error, nx.is_maximal_matching, G, {(0, 1, 2), (2, 3)}) + raises(error, nx.is_maximal_matching, G, {(0,), (2, 3)}) + + 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)}) + assert not nx.is_maximal_matching(G, {(0, 3)}) + G.add_edge(0, 0) + assert not nx.is_maximal_matching(G, {(0, 0)}) + + def test_not_maximal(self): + G = nx.path_graph(4) + assert not nx.is_maximal_matching(G, {(0, 1)}) + + +class TestIsPerfectMatching: + """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_invalid_input(self): + error = nx.NetworkXError + G = nx.path_graph(4) + # edge to node not in G + raises(error, nx.is_perfect_matching, G, {(0, 5)}) + raises(error, nx.is_perfect_matching, G, {(5, 0)}) + # edge not a 2-tuple + raises(error, nx.is_perfect_matching, G, {(0, 1, 2), (2, 3)}) + raises(error, nx.is_perfect_matching, G, {(0,), (2, 3)}) + + def test_selfloops(self): + error = nx.NetworkXError + G = nx.path_graph(4) + # selfloop for node not in G + raises(error, nx.is_perfect_matching, G, {(5, 5), (2, 3)}) + # selfloop edge not in G + assert not nx.is_perfect_matching(G, {(0, 0), (1, 2), (2, 3)}) + # selfloop edge in G + G.add_edge(0, 0) + assert not nx.is_perfect_matching(G, {(0, 0), (1, 2)}) + + def test_not_matching(self): + G = nx.path_graph(4) + assert not nx.is_perfect_matching(G, {(0, 3)}) + 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: + """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) + + def test_wrong_graph_type(self): + error = nx.NetworkXNotImplemented + raises(error, nx.maximal_matching, nx.MultiGraph()) + raises(error, nx.maximal_matching, nx.MultiDiGraph()) + raises(error, nx.maximal_matching, nx.DiGraph()) |