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

author shellac Mon, 22 Mar 2021 18:12:50 +0000
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```--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/env/lib/python3.9/site-packages/networkx/algorithms/bipartite/tests/test_matching.py	Mon Mar 22 18:12:50 2021 +0000
@@ -0,0 +1,316 @@
+"""Unit tests for the :mod:`networkx.algorithms.bipartite.matching` module."""
+import itertools
+
+import networkx as nx
+
+import pytest
+
+from networkx.algorithms.bipartite.matching import eppstein_matching
+from networkx.algorithms.bipartite.matching import hopcroft_karp_matching
+from networkx.algorithms.bipartite.matching import maximum_matching
+from networkx.algorithms.bipartite.matching import minimum_weight_full_matching
+from networkx.algorithms.bipartite.matching import to_vertex_cover
+
+
+class TestMatching:
+    """Tests for bipartite matching algorithms."""
+
+    def setup(self):
+        """Creates a bipartite graph for use in testing matching algorithms.
+
+        The bipartite graph has a maximum cardinality matching that leaves
+        vertex 1 and vertex 10 unmatched. The first six numbers are the left
+        vertices and the next six numbers are the right vertices.
+
+        """
+        self.simple_graph = nx.complete_bipartite_graph(2, 3)
+        self.simple_solution = {0: 2, 1: 3, 2: 0, 3: 1}
+
+        edges = [(0, 7), (0, 8), (2, 6), (2, 9), (3, 8), (4, 8), (4, 9), (5, 11)]
+        self.top_nodes = set(range(6))
+        self.graph = nx.Graph()
+
+        # Example bipartite graph from issue 2127
+        G = nx.Graph()
+            [
+                (1, "C"),
+                (1, "B"),
+                (0, "G"),
+                (1, "F"),
+                (1, "E"),
+                (0, "C"),
+                (1, "D"),
+                (1, "I"),
+                (0, "A"),
+                (0, "D"),
+                (0, "F"),
+                (0, "E"),
+                (0, "H"),
+                (1, "G"),
+                (1, "A"),
+                (0, "I"),
+                (0, "B"),
+                (1, "H"),
+            ]
+        )
+        self.disconnected_graph = G
+
+    def check_match(self, matching):
+        """Asserts that the matching is what we expect from the bipartite graph
+        constructed in the :meth:`setup` fixture.
+
+        """
+        # For the sake of brevity, rename `matching` to `M`.
+        M = matching
+        matched_vertices = frozenset(itertools.chain(*M.items()))
+        # Assert that the maximum number of vertices (10) is matched.
+        assert matched_vertices == frozenset(range(12)) - {1, 10}
+        # Assert that no vertex appears in two edges, or in other words, that
+        # the matching (u, v) and (v, u) both appear in the matching
+        # dictionary.
+        assert all(u == M[M[u]] for u in range(12) if u in M)
+
+    def check_vertex_cover(self, vertices):
+        """Asserts that the given set of vertices is the vertex cover we
+        expected from the bipartite graph constructed in the :meth:`setup`
+        fixture.
+
+        """
+        # By Konig's theorem, the number of edges in a maximum matching equals
+        # the number of vertices in a minimum vertex cover.
+        assert len(vertices) == 5
+        # Assert that the set is truly a vertex cover.
+        for (u, v) in self.graph.edges():
+            assert u in vertices or v in vertices
+        # TODO Assert that the vertices are the correct ones.
+
+    def test_eppstein_matching(self):
+        """Tests that David Eppstein's implementation of the Hopcroft--Karp
+        algorithm produces a maximum cardinality matching.
+
+        """
+        self.check_match(eppstein_matching(self.graph, self.top_nodes))
+
+    def test_hopcroft_karp_matching(self):
+        """Tests that the Hopcroft--Karp algorithm produces a maximum
+        cardinality matching in a bipartite graph.
+
+        """
+        self.check_match(hopcroft_karp_matching(self.graph, self.top_nodes))
+
+    def test_to_vertex_cover(self):
+        """Test for converting a maximum matching to a minimum vertex cover."""
+        matching = maximum_matching(self.graph, self.top_nodes)
+        vertex_cover = to_vertex_cover(self.graph, matching, self.top_nodes)
+        self.check_vertex_cover(vertex_cover)
+
+    def test_eppstein_matching_simple(self):
+        match = eppstein_matching(self.simple_graph)
+        assert match == self.simple_solution
+
+    def test_hopcroft_karp_matching_simple(self):
+        match = hopcroft_karp_matching(self.simple_graph)
+        assert match == self.simple_solution
+
+    def test_eppstein_matching_disconnected(self):
+        with pytest.raises(nx.AmbiguousSolution):
+            match = eppstein_matching(self.disconnected_graph)
+
+    def test_hopcroft_karp_matching_disconnected(self):
+        with pytest.raises(nx.AmbiguousSolution):
+            match = hopcroft_karp_matching(self.disconnected_graph)
+
+    def test_issue_2127(self):
+        """Test from issue 2127"""
+        # Build the example DAG
+        G = nx.DiGraph()
+
+        tc = nx.transitive_closure(G)
+        btc = nx.Graph()
+
+        # Create a bipartite graph based on the transitive closure of G
+        for v in tc.nodes():
+
+        for u, v in tc.edges():
+
+        top_nodes = {n for n in btc if n[0] == 0}
+        matching = hopcroft_karp_matching(btc, top_nodes)
+        vertex_cover = to_vertex_cover(btc, matching, top_nodes)
+        independent_set = set(G) - {v for _, v in vertex_cover}
+        assert {"B", "D", "F", "I", "H"} == independent_set
+
+    def test_vertex_cover_issue_2384(self):
+        G = nx.Graph([(0, 3), (1, 3), (1, 4), (2, 3)])
+        matching = maximum_matching(G)
+        vertex_cover = to_vertex_cover(G, matching)
+        for u, v in G.edges():
+            assert u in vertex_cover or v in vertex_cover
+
+    def test_unorderable_nodes(self):
+        a = object()
+        b = object()
+        c = object()
+        d = object()
+        e = object()
+        G = nx.Graph([(a, d), (b, d), (b, e), (c, d)])
+        matching = maximum_matching(G)
+        vertex_cover = to_vertex_cover(G, matching)
+        for u, v in G.edges():
+            assert u in vertex_cover or v in vertex_cover
+
+
+def test_eppstein_matching():
+    """Test in accordance to issue #1927"""
+    G = nx.Graph()
+    G.add_nodes_from(["a", 2, 3, 4], bipartite=0)
+    G.add_edges_from([("a", 1), ("a", "b"), (2, "b"), (2, "c"), (3, "c"), (4, 1)])
+    matching = eppstein_matching(G)
+    assert len(matching) == len(maximum_matching(G))
+    assert all(x in set(matching.keys()) for x in set(matching.values()))
+
+
+class TestMinimumWeightFullMatching:
+    @classmethod
+    def setup_class(cls):
+        global scipy
+        scipy = pytest.importorskip("scipy")
+
+    def test_minimum_weight_full_matching_incomplete_graph(self):
+        B = nx.Graph()
+        matching = minimum_weight_full_matching(B)
+        assert matching == {1: 4, 2: 3, 4: 1, 3: 2}
+
+    def test_minimum_weight_full_matching_with_no_full_matching(self):
+        B = nx.Graph()
+        with pytest.raises(ValueError):
+            minimum_weight_full_matching(B)
+
+    def test_minimum_weight_full_matching_square(self):
+        G = nx.complete_bipartite_graph(3, 3)
+        matching = minimum_weight_full_matching(G)
+        assert matching == {0: 4, 1: 3, 2: 5, 4: 0, 3: 1, 5: 2}
+
+    def test_minimum_weight_full_matching_smaller_left(self):
+        G = nx.complete_bipartite_graph(3, 4)
+        matching = minimum_weight_full_matching(G)
+        assert matching == {0: 4, 1: 6, 2: 5, 4: 0, 5: 2, 6: 1}
+
+    def test_minimum_weight_full_matching_smaller_top_nodes_right(self):
+        G = nx.complete_bipartite_graph(3, 4)
+        matching = minimum_weight_full_matching(G, top_nodes=[3, 4, 5, 6])
+        assert matching == {0: 4, 1: 6, 2: 5, 4: 0, 5: 2, 6: 1}
+
+    def test_minimum_weight_full_matching_smaller_right(self):
+        G = nx.complete_bipartite_graph(4, 3)
+        matching = minimum_weight_full_matching(G)
+        assert matching == {1: 4, 2: 6, 3: 5, 4: 1, 5: 3, 6: 2}
+
+    def test_minimum_weight_full_matching_negative_weights(self):
+        G = nx.complete_bipartite_graph(2, 2)