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+import pytest
+
+import networkx as nx
+
+
+class TestTriangles:
+ def test_empty(self):
+ G = nx.Graph()
+ assert list(nx.triangles(G).values()) == []
+
+ def test_path(self):
+ G = nx.path_graph(10)
+ assert list(nx.triangles(G).values()) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
+ assert nx.triangles(G) == {
+ 0: 0,
+ 1: 0,
+ 2: 0,
+ 3: 0,
+ 4: 0,
+ 5: 0,
+ 6: 0,
+ 7: 0,
+ 8: 0,
+ 9: 0,
+ }
+
+ def test_cubical(self):
+ G = nx.cubical_graph()
+ assert list(nx.triangles(G).values()) == [0, 0, 0, 0, 0, 0, 0, 0]
+ assert nx.triangles(G, 1) == 0
+ assert list(nx.triangles(G, [1, 2]).values()) == [0, 0]
+ assert nx.triangles(G, 1) == 0
+ assert nx.triangles(G, [1, 2]) == {1: 0, 2: 0}
+
+ def test_k5(self):
+ G = nx.complete_graph(5)
+ assert list(nx.triangles(G).values()) == [6, 6, 6, 6, 6]
+ assert sum(nx.triangles(G).values()) / 3 == 10
+ assert nx.triangles(G, 1) == 6
+ G.remove_edge(1, 2)
+ assert list(nx.triangles(G).values()) == [5, 3, 3, 5, 5]
+ assert nx.triangles(G, 1) == 3
+ G.add_edge(3, 3) # ignore self-edges
+ assert list(nx.triangles(G).values()) == [5, 3, 3, 5, 5]
+ assert nx.triangles(G, 3) == 5
+
+
+class TestDirectedClustering:
+ def test_clustering(self):
+ G = nx.DiGraph()
+ assert list(nx.clustering(G).values()) == []
+ assert nx.clustering(G) == {}
+
+ def test_path(self):
+ G = nx.path_graph(10, create_using=nx.DiGraph())
+ assert list(nx.clustering(G).values()) == [
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ ]
+ assert nx.clustering(G) == {
+ 0: 0,
+ 1: 0,
+ 2: 0,
+ 3: 0,
+ 4: 0,
+ 5: 0,
+ 6: 0,
+ 7: 0,
+ 8: 0,
+ 9: 0,
+ }
+ assert nx.clustering(G, 0) == 0
+
+ def test_k5(self):
+ G = nx.complete_graph(5, create_using=nx.DiGraph())
+ assert list(nx.clustering(G).values()) == [1, 1, 1, 1, 1]
+ assert nx.average_clustering(G) == 1
+ G.remove_edge(1, 2)
+ assert list(nx.clustering(G).values()) == [
+ 11 / 12,
+ 1,
+ 1,
+ 11 / 12,
+ 11 / 12,
+ ]
+ assert nx.clustering(G, [1, 4]) == {1: 1, 4: 11 / 12}
+ G.remove_edge(2, 1)
+ assert list(nx.clustering(G).values()) == [
+ 5 / 6,
+ 1,
+ 1,
+ 5 / 6,
+ 5 / 6,
+ ]
+ assert nx.clustering(G, [1, 4]) == {1: 1, 4: 0.83333333333333337}
+ assert nx.clustering(G, 4) == 5 / 6
+
+ def test_triangle_and_edge(self):
+ G = nx.cycle_graph(3, create_using=nx.DiGraph())
+ G.add_edge(0, 4)
+ assert nx.clustering(G)[0] == 1 / 6
+
+
+class TestDirectedWeightedClustering:
+ @classmethod
+ def setup_class(cls):
+ global np
+ np = pytest.importorskip("numpy")
+
+ def test_clustering(self):
+ G = nx.DiGraph()
+ assert list(nx.clustering(G, weight="weight").values()) == []
+ assert nx.clustering(G) == {}
+
+ def test_path(self):
+ G = nx.path_graph(10, create_using=nx.DiGraph())
+ assert list(nx.clustering(G, weight="weight").values()) == [
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ ]
+ assert nx.clustering(G, weight="weight") == {
+ 0: 0,
+ 1: 0,
+ 2: 0,
+ 3: 0,
+ 4: 0,
+ 5: 0,
+ 6: 0,
+ 7: 0,
+ 8: 0,
+ 9: 0,
+ }
+
+ def test_k5(self):
+ G = nx.complete_graph(5, create_using=nx.DiGraph())
+ assert list(nx.clustering(G, weight="weight").values()) == [1, 1, 1, 1, 1]
+ assert nx.average_clustering(G, weight="weight") == 1
+ G.remove_edge(1, 2)
+ assert list(nx.clustering(G, weight="weight").values()) == [
+ 11 / 12,
+ 1,
+ 1,
+ 11 / 12,
+ 11 / 12,
+ ]
+ assert nx.clustering(G, [1, 4], weight="weight") == {1: 1, 4: 11 / 12}
+ G.remove_edge(2, 1)
+ assert list(nx.clustering(G, weight="weight").values()) == [
+ 5 / 6,
+ 1,
+ 1,
+ 5 / 6,
+ 5 / 6,
+ ]
+ assert nx.clustering(G, [1, 4], weight="weight") == {
+ 1: 1,
+ 4: 0.83333333333333337,
+ }
+
+ def test_triangle_and_edge(self):
+ G = nx.cycle_graph(3, create_using=nx.DiGraph())
+ G.add_edge(0, 4, weight=2)
+ assert nx.clustering(G)[0] == 1 / 6
+ # Relaxed comparisons to allow graphblas-algorithms to pass tests
+ np.testing.assert_allclose(nx.clustering(G, weight="weight")[0], 1 / 12)
+ np.testing.assert_allclose(nx.clustering(G, 0, weight="weight"), 1 / 12)
+
+
+class TestWeightedClustering:
+ @classmethod
+ def setup_class(cls):
+ global np
+ np = pytest.importorskip("numpy")
+
+ def test_clustering(self):
+ G = nx.Graph()
+ assert list(nx.clustering(G, weight="weight").values()) == []
+ assert nx.clustering(G) == {}
+
+ def test_path(self):
+ G = nx.path_graph(10)
+ assert list(nx.clustering(G, weight="weight").values()) == [
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ ]
+ assert nx.clustering(G, weight="weight") == {
+ 0: 0,
+ 1: 0,
+ 2: 0,
+ 3: 0,
+ 4: 0,
+ 5: 0,
+ 6: 0,
+ 7: 0,
+ 8: 0,
+ 9: 0,
+ }
+
+ def test_cubical(self):
+ G = nx.cubical_graph()
+ assert list(nx.clustering(G, weight="weight").values()) == [
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ ]
+ assert nx.clustering(G, 1) == 0
+ assert list(nx.clustering(G, [1, 2], weight="weight").values()) == [0, 0]
+ assert nx.clustering(G, 1, weight="weight") == 0
+ assert nx.clustering(G, [1, 2], weight="weight") == {1: 0, 2: 0}
+
+ def test_k5(self):
+ G = nx.complete_graph(5)
+ assert list(nx.clustering(G, weight="weight").values()) == [1, 1, 1, 1, 1]
+ assert nx.average_clustering(G, weight="weight") == 1
+ G.remove_edge(1, 2)
+ assert list(nx.clustering(G, weight="weight").values()) == [
+ 5 / 6,
+ 1,
+ 1,
+ 5 / 6,
+ 5 / 6,
+ ]
+ assert nx.clustering(G, [1, 4], weight="weight") == {
+ 1: 1,
+ 4: 0.83333333333333337,
+ }
+
+ def test_triangle_and_edge(self):
+ G = nx.cycle_graph(3)
+ G.add_edge(0, 4, weight=2)
+ assert nx.clustering(G)[0] == 1 / 3
+ np.testing.assert_allclose(nx.clustering(G, weight="weight")[0], 1 / 6)
+ np.testing.assert_allclose(nx.clustering(G, 0, weight="weight"), 1 / 6)
+
+ def test_triangle_and_signed_edge(self):
+ G = nx.cycle_graph(3)
+ G.add_edge(0, 1, weight=-1)
+ G.add_edge(3, 0, weight=0)
+ assert nx.clustering(G)[0] == 1 / 3
+ assert nx.clustering(G, weight="weight")[0] == -1 / 3
+
+
+class TestClustering:
+ @classmethod
+ def setup_class(cls):
+ pytest.importorskip("numpy")
+
+ def test_clustering(self):
+ G = nx.Graph()
+ assert list(nx.clustering(G).values()) == []
+ assert nx.clustering(G) == {}
+
+ def test_path(self):
+ G = nx.path_graph(10)
+ assert list(nx.clustering(G).values()) == [
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ ]
+ assert nx.clustering(G) == {
+ 0: 0,
+ 1: 0,
+ 2: 0,
+ 3: 0,
+ 4: 0,
+ 5: 0,
+ 6: 0,
+ 7: 0,
+ 8: 0,
+ 9: 0,
+ }
+
+ def test_cubical(self):
+ G = nx.cubical_graph()
+ assert list(nx.clustering(G).values()) == [0, 0, 0, 0, 0, 0, 0, 0]
+ assert nx.clustering(G, 1) == 0
+ assert list(nx.clustering(G, [1, 2]).values()) == [0, 0]
+ assert nx.clustering(G, 1) == 0
+ assert nx.clustering(G, [1, 2]) == {1: 0, 2: 0}
+
+ def test_k5(self):
+ G = nx.complete_graph(5)
+ assert list(nx.clustering(G).values()) == [1, 1, 1, 1, 1]
+ assert nx.average_clustering(G) == 1
+ G.remove_edge(1, 2)
+ assert list(nx.clustering(G).values()) == [
+ 5 / 6,
+ 1,
+ 1,
+ 5 / 6,
+ 5 / 6,
+ ]
+ assert nx.clustering(G, [1, 4]) == {1: 1, 4: 0.83333333333333337}
+
+ def test_k5_signed(self):
+ G = nx.complete_graph(5)
+ assert list(nx.clustering(G).values()) == [1, 1, 1, 1, 1]
+ assert nx.average_clustering(G) == 1
+ G.remove_edge(1, 2)
+ G.add_edge(0, 1, weight=-1)
+ assert list(nx.clustering(G, weight="weight").values()) == [
+ 1 / 6,
+ -1 / 3,
+ 1,
+ 3 / 6,
+ 3 / 6,
+ ]
+
+
+class TestTransitivity:
+ def test_transitivity(self):
+ G = nx.Graph()
+ assert nx.transitivity(G) == 0
+
+ def test_path(self):
+ G = nx.path_graph(10)
+ assert nx.transitivity(G) == 0
+
+ def test_cubical(self):
+ G = nx.cubical_graph()
+ assert nx.transitivity(G) == 0
+
+ def test_k5(self):
+ G = nx.complete_graph(5)
+ assert nx.transitivity(G) == 1
+ G.remove_edge(1, 2)
+ assert nx.transitivity(G) == 0.875
+
+
+class TestSquareClustering:
+ def test_clustering(self):
+ G = nx.Graph()
+ assert list(nx.square_clustering(G).values()) == []
+ assert nx.square_clustering(G) == {}
+
+ def test_path(self):
+ G = nx.path_graph(10)
+ assert list(nx.square_clustering(G).values()) == [
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ ]
+ assert nx.square_clustering(G) == {
+ 0: 0,
+ 1: 0,
+ 2: 0,
+ 3: 0,
+ 4: 0,
+ 5: 0,
+ 6: 0,
+ 7: 0,
+ 8: 0,
+ 9: 0,
+ }
+
+ def test_cubical(self):
+ G = nx.cubical_graph()
+ assert list(nx.square_clustering(G).values()) == [
+ 1 / 3,
+ 1 / 3,
+ 1 / 3,
+ 1 / 3,
+ 1 / 3,
+ 1 / 3,
+ 1 / 3,
+ 1 / 3,
+ ]
+ assert list(nx.square_clustering(G, [1, 2]).values()) == [1 / 3, 1 / 3]
+ assert nx.square_clustering(G, [1])[1] == 1 / 3
+ assert nx.square_clustering(G, 1) == 1 / 3
+ assert nx.square_clustering(G, [1, 2]) == {1: 1 / 3, 2: 1 / 3}
+
+ def test_k5(self):
+ G = nx.complete_graph(5)
+ assert list(nx.square_clustering(G).values()) == [1, 1, 1, 1, 1]
+
+ def test_bipartite_k5(self):
+ G = nx.complete_bipartite_graph(5, 5)
+ assert list(nx.square_clustering(G).values()) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
+
+ def test_lind_square_clustering(self):
+ """Test C4 for figure 1 Lind et al (2005)"""
+ G = nx.Graph(
+ [
+ (1, 2),
+ (1, 3),
+ (1, 6),
+ (1, 7),
+ (2, 4),
+ (2, 5),
+ (3, 4),
+ (3, 5),
+ (6, 7),
+ (7, 8),
+ (6, 8),
+ (7, 9),
+ (7, 10),
+ (6, 11),
+ (6, 12),
+ (2, 13),
+ (2, 14),
+ (3, 15),
+ (3, 16),
+ ]
+ )
+ G1 = G.subgraph([1, 2, 3, 4, 5, 13, 14, 15, 16])
+ G2 = G.subgraph([1, 6, 7, 8, 9, 10, 11, 12])
+ assert nx.square_clustering(G, [1])[1] == 3 / 43
+ assert nx.square_clustering(G1, [1])[1] == 2 / 6
+ assert nx.square_clustering(G2, [1])[1] == 1 / 5
+
+ def test_peng_square_clustering(self):
+ """Test eq2 for figure 1 Peng et al (2008)"""
+ G = nx.Graph([(1, 2), (1, 3), (2, 4), (3, 4), (3, 5), (3, 6)])
+ assert nx.square_clustering(G, [1])[1] == 1 / 3
+
+ def test_self_loops_square_clustering(self):
+ G = nx.path_graph(5)
+ assert nx.square_clustering(G) == {0: 0, 1: 0.0, 2: 0.0, 3: 0.0, 4: 0}
+ G.add_edges_from([(0, 0), (1, 1), (2, 2)])
+ assert nx.square_clustering(G) == {0: 1, 1: 0.5, 2: 0.2, 3: 0.0, 4: 0}
+
+
+class TestAverageClustering:
+ @classmethod
+ def setup_class(cls):
+ pytest.importorskip("numpy")
+
+ def test_empty(self):
+ G = nx.Graph()
+ with pytest.raises(ZeroDivisionError):
+ nx.average_clustering(G)
+
+ def test_average_clustering(self):
+ G = nx.cycle_graph(3)
+ G.add_edge(2, 3)
+ assert nx.average_clustering(G) == (1 + 1 + 1 / 3) / 4
+ assert nx.average_clustering(G, count_zeros=True) == (1 + 1 + 1 / 3) / 4
+ assert nx.average_clustering(G, count_zeros=False) == (1 + 1 + 1 / 3) / 3
+ assert nx.average_clustering(G, [1, 2, 3]) == (1 + 1 / 3) / 3
+ assert nx.average_clustering(G, [1, 2, 3], count_zeros=True) == (1 + 1 / 3) / 3
+ assert nx.average_clustering(G, [1, 2, 3], count_zeros=False) == (1 + 1 / 3) / 2
+
+ def test_average_clustering_signed(self):
+ G = nx.cycle_graph(3)
+ G.add_edge(2, 3)
+ G.add_edge(0, 1, weight=-1)
+ assert nx.average_clustering(G, weight="weight") == (-1 - 1 - 1 / 3) / 4
+ assert (
+ nx.average_clustering(G, weight="weight", count_zeros=True)
+ == (-1 - 1 - 1 / 3) / 4
+ )
+ assert (
+ nx.average_clustering(G, weight="weight", count_zeros=False)
+ == (-1 - 1 - 1 / 3) / 3
+ )
+
+
+class TestDirectedAverageClustering:
+ @classmethod
+ def setup_class(cls):
+ pytest.importorskip("numpy")
+
+ def test_empty(self):
+ G = nx.DiGraph()
+ with pytest.raises(ZeroDivisionError):
+ nx.average_clustering(G)
+
+ def test_average_clustering(self):
+ G = nx.cycle_graph(3, create_using=nx.DiGraph())
+ G.add_edge(2, 3)
+ assert nx.average_clustering(G) == (1 + 1 + 1 / 3) / 8
+ assert nx.average_clustering(G, count_zeros=True) == (1 + 1 + 1 / 3) / 8
+ assert nx.average_clustering(G, count_zeros=False) == (1 + 1 + 1 / 3) / 6
+ assert nx.average_clustering(G, [1, 2, 3]) == (1 + 1 / 3) / 6
+ assert nx.average_clustering(G, [1, 2, 3], count_zeros=True) == (1 + 1 / 3) / 6
+ assert nx.average_clustering(G, [1, 2, 3], count_zeros=False) == (1 + 1 / 3) / 4
+
+
+class TestGeneralizedDegree:
+ def test_generalized_degree(self):
+ G = nx.Graph()
+ assert nx.generalized_degree(G) == {}
+
+ def test_path(self):
+ G = nx.path_graph(5)
+ assert nx.generalized_degree(G, 0) == {0: 1}
+ assert nx.generalized_degree(G, 1) == {0: 2}
+
+ def test_cubical(self):
+ G = nx.cubical_graph()
+ assert nx.generalized_degree(G, 0) == {0: 3}
+
+ def test_k5(self):
+ G = nx.complete_graph(5)
+ assert nx.generalized_degree(G, 0) == {3: 4}
+ G.remove_edge(0, 1)
+ assert nx.generalized_degree(G, 0) == {2: 3}
+ assert nx.generalized_degree(G, [1, 2]) == {1: {2: 3}, 2: {2: 2, 3: 2}}
+ assert nx.generalized_degree(G) == {
+ 0: {2: 3},
+ 1: {2: 3},
+ 2: {2: 2, 3: 2},
+ 3: {2: 2, 3: 2},
+ 4: {2: 2, 3: 2},
+ }
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