import math
from itertools import permutations
import pytest
import networkx as nx
from networkx.utils import edges_equal
@pytest.mark.parametrize(
"fn", (nx.is_matching, nx.is_maximal_matching, nx.is_perfect_matching)
)
@pytest.mark.parametrize(
"edgeset",
(
{(0, 5)}, # Single edge, node not in G
{(5, 0)}, # for both edge orders
{(0, 5), (2, 3)}, # node not in G, but other edge is valid matching
{(5, 5), (2, 3)}, # Self-loop hits node not in G validation first
),
)
def test_is_matching_node_not_in_G(fn, edgeset):
"""All is_*matching functions have consistent exception message for node
not in G."""
G = nx.path_graph(4)
with pytest.raises(nx.NetworkXError, match="matching.*with node not in G"):
fn(G, edgeset)
@pytest.mark.parametrize(
"fn", (nx.is_matching, nx.is_maximal_matching, nx.is_perfect_matching)
)
@pytest.mark.parametrize(
"edgeset",
(
{(0, 1, 2), (2, 3)}, # 3-tuple
{(0,), (2, 3)}, # 1-tuple
),
)
def test_is_matching_invalid_edge(fn, edgeset):
"""All is_*matching functions have consistent exception message for invalid
edges in matching."""
G = nx.path_graph(4)
with pytest.raises(nx.NetworkXError, match=".*non-2-tuple edge.*"):
fn(G, edgeset)
@pytest.mark.parametrize("graph_type", (nx.MultiGraph, nx.DiGraph, nx.MultiDiGraph))
@pytest.mark.parametrize(
"fn", (nx.max_weight_matching, nx.min_weight_matching, nx.maximal_matching)
)
def test_wrong_graph_type(fn, graph_type):
G = graph_type()
with pytest.raises(nx.NetworkXNotImplemented):
fn(G)
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), {(0, 1)})
assert edges_equal(nx.min_weight_matching(G), {(0, 1)})
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), {("two", "three")})
assert edges_equal(nx.min_weight_matching(G), {("one", "two")})
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), {(2, 3)})
assert edges_equal(nx.max_weight_matching(G, weight=None), {(1, 2), (3, 4)})
assert edges_equal(nx.min_weight_matching(G), {(1, 2), (3, 4)})
assert edges_equal(nx.min_weight_matching(G, weight=None), {(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), {(1, 2), (3, 4)})
assert edges_equal(nx.min_weight_matching(G), {(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"), {("one", "two")})
assert edges_equal(nx.min_weight_matching(G, weight="abcd"), {("two", "three")})
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), {(1, 4), (2, 3)})
assert edges_equal(nx.min_weight_matching(G), {(1, 4), (2, 3)})
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), {(1, 2)})
assert edges_equal(
nx.max_weight_matching(G, maxcardinality=True), {(1, 3), (2, 4)}
)
assert edges_equal(nx.min_weight_matching(G), {(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 = {(1, 2), (3, 4)}
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 = {(1, 6), (2, 3), (4, 5)}
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 = {(1, 6), (2, 3), (4, 5)}
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 = {(1, 2), (3, 6), (4, 5)}
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),
]
)
expected_edgeset = {(1, 3), (2, 4), (5, 6)}
expected = {frozenset(e) for e in expected_edgeset}
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 = {(1, 2), (3, 4), (5, 6), (7, 8)}
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 = {(1, 2), (3, 5), (4, 6), (7, 8)}
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 = {(1, 6), (2, 3), (4, 8), (5, 7)}
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 = {(1, 8), (2, 3), (4, 7), (5, 6)}
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),
]
)
answer = {(1, 6), (2, 3), (4, 8), (5, 7), (9, 10)}
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),
]
)
answer = {(1, 6), (2, 3), (4, 8), (5, 7), (9, 10)}
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),
]
)
answer = {(1, 6), (2, 3), (4, 8), (5, 7), (9, 10)}
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),
]
)
answer = {(1, 8), (2, 3), (4, 6), (5, 9), (7, 10), (11, 12)}
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),
]
)
answer = {(1, 2), (3, 5), (4, 9), (6, 7), (8, 10)}
assert edges_equal(nx.max_weight_matching(G), answer)
assert edges_equal(nx.min_weight_matching(G), answer)
def test_min_weight_matching_max_cardinality(self):
G = nx.Graph()
G.add_weighted_edges_from([(1, 2, 1000), (2, 3, 2), (3, 4, 3000)])
# The minimum-weight maximal matching is {(2, 3)}; the minimum-weight
# maximum-cardinality matching is {(1, 2), (3, 4)}. See gh-8062.
answer = {(1, 2), (3, 4)}
assert edges_equal(nx.min_weight_matching(G), answer)
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_selfloops(self):
G = nx.path_graph(4)
# 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)})
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_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_selfloops(self):
G = nx.path_graph(4)
# 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)