### view env/lib/python3.9/site-packages/networkx/algorithms/tests/test_matching.py @ 0:4f3585e2f14bdraftdefaulttip

"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
author shellac Mon, 22 Mar 2021 18:12:50 +0000
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```
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:
"""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:
"""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:
"""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:
"""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:
"""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)
```