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pythonProject/.venv/Lib/site-packages/networkx/algorithms/centrality/tests/test_dispersion.py

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+import networkx as nx
+
+
+def small_ego_G():
+    """The sample network from https://arxiv.org/pdf/1310.6753v1.pdf"""
+    edges = [
+        ("a", "b"),
+        ("a", "c"),
+        ("b", "c"),
+        ("b", "d"),
+        ("b", "e"),
+        ("b", "f"),
+        ("c", "d"),
+        ("c", "f"),
+        ("c", "h"),
+        ("d", "f"),
+        ("e", "f"),
+        ("f", "h"),
+        ("h", "j"),
+        ("h", "k"),
+        ("i", "j"),
+        ("i", "k"),
+        ("j", "k"),
+        ("u", "a"),
+        ("u", "b"),
+        ("u", "c"),
+        ("u", "d"),
+        ("u", "e"),
+        ("u", "f"),
+        ("u", "g"),
+        ("u", "h"),
+        ("u", "i"),
+        ("u", "j"),
+        ("u", "k"),
+    ]
+    G = nx.Graph()
+    G.add_edges_from(edges)
+
+    return G
+
+
+class TestDispersion:
+    def test_article(self):
+        """our algorithm matches article's"""
+        G = small_ego_G()
+        disp_uh = nx.dispersion(G, "u", "h", normalized=False)
+        disp_ub = nx.dispersion(G, "u", "b", normalized=False)
+        assert disp_uh == 4
+        assert disp_ub == 1
+
+    def test_results_length(self):
+        """there is a result for every node"""
+        G = small_ego_G()
+        disp = nx.dispersion(G)
+        disp_Gu = nx.dispersion(G, "u")
+        disp_uv = nx.dispersion(G, "u", "h")
+        assert len(disp) == len(G)
+        assert len(disp_Gu) == len(G) - 1
+        assert isinstance(disp_uv, float)
+
+    def test_dispersion_v_only(self):
+        G = small_ego_G()
+        disp_G_h = nx.dispersion(G, v="h", normalized=False)
+        disp_G_h_normalized = nx.dispersion(G, v="h", normalized=True)
+        assert disp_G_h == {"c": 0, "f": 0, "j": 0, "k": 0, "u": 4}
+        assert disp_G_h_normalized == {"c": 0.0, "f": 0.0, "j": 0.0, "k": 0.0, "u": 1.0}
+
+    def test_impossible_things(self):
+        G = nx.karate_club_graph()
+        disp = nx.dispersion(G)
+        for u in disp:
+            for v in disp[u]:
+                assert disp[u][v] >= 0

pythonProject/.venv/Lib/site-packages/networkx/algorithms/centrality/tests/test_eigenvector_centrality.py

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+import math
+
+import pytest
+
+np = pytest.importorskip("numpy")
+pytest.importorskip("scipy")
+
+
+import networkx as nx
+
+
+class TestEigenvectorCentrality:
+    def test_K5(self):
+        """Eigenvector centrality: K5"""
+        G = nx.complete_graph(5)
+        b = nx.eigenvector_centrality(G)
+        v = math.sqrt(1 / 5.0)
+        b_answer = dict.fromkeys(G, v)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+        nstart = {n: 1 for n in G}
+        b = nx.eigenvector_centrality(G, nstart=nstart)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+        b = nx.eigenvector_centrality_numpy(G)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-3)
+
+    def test_P3(self):
+        """Eigenvector centrality: P3"""
+        G = nx.path_graph(3)
+        b_answer = {0: 0.5, 1: 0.7071, 2: 0.5}
+        b = nx.eigenvector_centrality_numpy(G)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-4)
+        b = nx.eigenvector_centrality(G)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-4)
+
+    def test_P3_unweighted(self):
+        """Eigenvector centrality: P3"""
+        G = nx.path_graph(3)
+        b_answer = {0: 0.5, 1: 0.7071, 2: 0.5}
+        b = nx.eigenvector_centrality_numpy(G, weight=None)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-4)
+
+    def test_maxiter(self):
+        with pytest.raises(nx.PowerIterationFailedConvergence):
+            G = nx.path_graph(3)
+            nx.eigenvector_centrality(G, max_iter=0)
+
+
+class TestEigenvectorCentralityDirected:
+    @classmethod
+    def setup_class(cls):
+        G = nx.DiGraph()
+
+        edges = [
+            (1, 2),
+            (1, 3),
+            (2, 4),
+            (3, 2),
+            (3, 5),
+            (4, 2),
+            (4, 5),
+            (4, 6),
+            (5, 6),
+            (5, 7),
+            (5, 8),
+            (6, 8),
+            (7, 1),
+            (7, 5),
+            (7, 8),
+            (8, 6),
+            (8, 7),
+        ]
+
+        G.add_edges_from(edges, weight=2.0)
+        cls.G = G.reverse()
+        cls.G.evc = [
+            0.25368793,
+            0.19576478,
+            0.32817092,
+            0.40430835,
+            0.48199885,
+            0.15724483,
+            0.51346196,
+            0.32475403,
+        ]
+
+        H = nx.DiGraph()
+
+        edges = [
+            (1, 2),
+            (1, 3),
+            (2, 4),
+            (3, 2),
+            (3, 5),
+            (4, 2),
+            (4, 5),
+            (4, 6),
+            (5, 6),
+            (5, 7),
+            (5, 8),
+            (6, 8),
+            (7, 1),
+            (7, 5),
+            (7, 8),
+            (8, 6),
+            (8, 7),
+        ]
+
+        G.add_edges_from(edges)
+        cls.H = G.reverse()
+        cls.H.evc = [
+            0.25368793,
+            0.19576478,
+            0.32817092,
+            0.40430835,
+            0.48199885,
+            0.15724483,
+            0.51346196,
+            0.32475403,
+        ]
+
+    def test_eigenvector_centrality_weighted(self):
+        G = self.G
+        p = nx.eigenvector_centrality(G)
+        for a, b in zip(list(p.values()), self.G.evc):
+            assert a == pytest.approx(b, abs=1e-4)
+
+    def test_eigenvector_centrality_weighted_numpy(self):
+        G = self.G
+        p = nx.eigenvector_centrality_numpy(G)
+        for a, b in zip(list(p.values()), self.G.evc):
+            assert a == pytest.approx(b, abs=1e-7)
+
+    def test_eigenvector_centrality_unweighted(self):
+        G = self.H
+        p = nx.eigenvector_centrality(G)
+        for a, b in zip(list(p.values()), self.G.evc):
+            assert a == pytest.approx(b, abs=1e-4)
+
+    def test_eigenvector_centrality_unweighted_numpy(self):
+        G = self.H
+        p = nx.eigenvector_centrality_numpy(G)
+        for a, b in zip(list(p.values()), self.G.evc):
+            assert a == pytest.approx(b, abs=1e-7)
+
+
+class TestEigenvectorCentralityExceptions:
+    def test_multigraph(self):
+        with pytest.raises(nx.NetworkXException):
+            nx.eigenvector_centrality(nx.MultiGraph())
+
+    def test_multigraph_numpy(self):
+        with pytest.raises(nx.NetworkXException):
+            nx.eigenvector_centrality_numpy(nx.MultiGraph())
+
+    def test_empty(self):
+        with pytest.raises(nx.NetworkXException):
+            nx.eigenvector_centrality(nx.Graph())
+
+    def test_empty_numpy(self):
+        with pytest.raises(nx.NetworkXException):
+            nx.eigenvector_centrality_numpy(nx.Graph())
+
+    def test_zero_nstart(self):
+        G = nx.Graph([(1, 2), (1, 3), (2, 3)])
+        with pytest.raises(
+            nx.NetworkXException, match="initial vector cannot have all zero values"
+        ):
+            nx.eigenvector_centrality(G, nstart={v: 0 for v in G})

pythonProject/.venv/Lib/site-packages/networkx/algorithms/centrality/tests/test_group.py

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+"""
+Tests for Group Centrality Measures
+"""
+
+
+import pytest
+
+import networkx as nx
+
+
+class TestGroupBetweennessCentrality:
+    def test_group_betweenness_single_node(self):
+        """
+        Group betweenness centrality for single node group
+        """
+        G = nx.path_graph(5)
+        C = [1]
+        b = nx.group_betweenness_centrality(
+            G, C, weight=None, normalized=False, endpoints=False
+        )
+        b_answer = 3.0
+        assert b == b_answer
+
+    def test_group_betweenness_with_endpoints(self):
+        """
+        Group betweenness centrality for single node group
+        """
+        G = nx.path_graph(5)
+        C = [1]
+        b = nx.group_betweenness_centrality(
+            G, C, weight=None, normalized=False, endpoints=True
+        )
+        b_answer = 7.0
+        assert b == b_answer
+
+    def test_group_betweenness_normalized(self):
+        """
+        Group betweenness centrality for group with more than
+        1 node and normalized
+        """
+        G = nx.path_graph(5)
+        C = [1, 3]
+        b = nx.group_betweenness_centrality(
+            G, C, weight=None, normalized=True, endpoints=False
+        )
+        b_answer = 1.0
+        assert b == b_answer
+
+    def test_two_group_betweenness_value_zero(self):
+        """
+        Group betweenness centrality value of 0
+        """
+        G = nx.cycle_graph(7)
+        C = [[0, 1, 6], [0, 1, 5]]
+        b = nx.group_betweenness_centrality(G, C, weight=None, normalized=False)
+        b_answer = [0.0, 3.0]
+        assert b == b_answer
+
+    def test_group_betweenness_value_zero(self):
+        """
+        Group betweenness centrality value of 0
+        """
+        G = nx.cycle_graph(6)
+        C = [0, 1, 5]
+        b = nx.group_betweenness_centrality(G, C, weight=None, normalized=False)
+        b_answer = 0.0
+        assert b == b_answer
+
+    def test_group_betweenness_disconnected_graph(self):
+        """
+        Group betweenness centrality in a disconnected graph
+        """
+        G = nx.path_graph(5)
+        G.remove_edge(0, 1)
+        C = [1]
+        b = nx.group_betweenness_centrality(G, C, weight=None, normalized=False)
+        b_answer = 0.0
+        assert b == b_answer
+
+    def test_group_betweenness_node_not_in_graph(self):
+        """
+        Node(s) in C not in graph, raises NodeNotFound exception
+        """
+        with pytest.raises(nx.NodeNotFound):
+            nx.group_betweenness_centrality(nx.path_graph(5), [4, 7, 8])
+
+    def test_group_betweenness_directed_weighted(self):
+        """
+        Group betweenness centrality in a directed and weighted graph
+        """
+        G = nx.DiGraph()
+        G.add_edge(1, 0, weight=1)
+        G.add_edge(0, 2, weight=2)
+        G.add_edge(1, 2, weight=3)
+        G.add_edge(3, 1, weight=4)
+        G.add_edge(2, 3, weight=1)
+        G.add_edge(4, 3, weight=6)
+        G.add_edge(2, 4, weight=7)
+        C = [1, 2]
+        b = nx.group_betweenness_centrality(G, C, weight="weight", normalized=False)
+        b_answer = 5.0
+        assert b == b_answer
+
+
+class TestProminentGroup:
+    np = pytest.importorskip("numpy")
+    pd = pytest.importorskip("pandas")
+
+    def test_prominent_group_single_node(self):
+        """
+        Prominent group for single node
+        """
+        G = nx.path_graph(5)
+        k = 1
+        b, g = nx.prominent_group(G, k, normalized=False, endpoints=False)
+        b_answer, g_answer = 4.0, [2]
+        assert b == b_answer and g == g_answer
+
+    def test_prominent_group_with_c(self):
+        """
+        Prominent group without some nodes
+        """
+        G = nx.path_graph(5)
+        k = 1
+        b, g = nx.prominent_group(G, k, normalized=False, C=[2])
+        b_answer, g_answer = 3.0, [1]
+        assert b == b_answer and g == g_answer
+
+    def test_prominent_group_normalized_endpoints(self):
+        """
+        Prominent group with normalized result, with endpoints
+        """
+        G = nx.cycle_graph(7)
+        k = 2
+        b, g = nx.prominent_group(G, k, normalized=True, endpoints=True)
+        b_answer, g_answer = 1.7, [2, 5]
+        assert b == b_answer and g == g_answer
+
+    def test_prominent_group_disconnected_graph(self):
+        """
+        Prominent group of disconnected graph
+        """
+        G = nx.path_graph(6)
+        G.remove_edge(0, 1)
+        k = 1
+        b, g = nx.prominent_group(G, k, weight=None, normalized=False)
+        b_answer, g_answer = 4.0, [3]
+        assert b == b_answer and g == g_answer
+
+    def test_prominent_group_node_not_in_graph(self):
+        """
+        Node(s) in C not in graph, raises NodeNotFound exception
+        """
+        with pytest.raises(nx.NodeNotFound):
+            nx.prominent_group(nx.path_graph(5), 1, C=[10])
+
+    def test_group_betweenness_directed_weighted(self):
+        """
+        Group betweenness centrality in a directed and weighted graph
+        """
+        G = nx.DiGraph()
+        G.add_edge(1, 0, weight=1)
+        G.add_edge(0, 2, weight=2)
+        G.add_edge(1, 2, weight=3)
+        G.add_edge(3, 1, weight=4)
+        G.add_edge(2, 3, weight=1)
+        G.add_edge(4, 3, weight=6)
+        G.add_edge(2, 4, weight=7)
+        k = 2
+        b, g = nx.prominent_group(G, k, weight="weight", normalized=False)
+        b_answer, g_answer = 5.0, [1, 2]
+        assert b == b_answer and g == g_answer
+
+    def test_prominent_group_greedy_algorithm(self):
+        """
+        Group betweenness centrality in a greedy algorithm
+        """
+        G = nx.cycle_graph(7)
+        k = 2
+        b, g = nx.prominent_group(G, k, normalized=True, endpoints=True, greedy=True)
+        b_answer, g_answer = 1.7, [6, 3]
+        assert b == b_answer and g == g_answer
+
+
+class TestGroupClosenessCentrality:
+    def test_group_closeness_single_node(self):
+        """
+        Group closeness centrality for a single node group
+        """
+        G = nx.path_graph(5)
+        c = nx.group_closeness_centrality(G, [1])
+        c_answer = nx.closeness_centrality(G, 1)
+        assert c == c_answer
+
+    def test_group_closeness_disconnected(self):
+        """
+        Group closeness centrality for a disconnected graph
+        """
+        G = nx.Graph()
+        G.add_nodes_from([1, 2, 3, 4])
+        c = nx.group_closeness_centrality(G, [1, 2])
+        c_answer = 0
+        assert c == c_answer
+
+    def test_group_closeness_multiple_node(self):
+        """
+        Group closeness centrality for a group with more than
+        1 node
+        """
+        G = nx.path_graph(4)
+        c = nx.group_closeness_centrality(G, [1, 2])
+        c_answer = 1
+        assert c == c_answer
+
+    def test_group_closeness_node_not_in_graph(self):
+        """
+        Node(s) in S not in graph, raises NodeNotFound exception
+        """
+        with pytest.raises(nx.NodeNotFound):
+            nx.group_closeness_centrality(nx.path_graph(5), [6, 7, 8])
+
+
+class TestGroupDegreeCentrality:
+    def test_group_degree_centrality_single_node(self):
+        """
+        Group degree centrality for a single node group
+        """
+        G = nx.path_graph(4)
+        d = nx.group_degree_centrality(G, [1])
+        d_answer = nx.degree_centrality(G)[1]
+        assert d == d_answer
+
+    def test_group_degree_centrality_multiple_node(self):
+        """
+        Group degree centrality for group with more than
+        1 node
+        """
+        G = nx.Graph()
+        G.add_nodes_from([1, 2, 3, 4, 5, 6, 7, 8])
+        G.add_edges_from(
+            [(1, 2), (1, 3), (1, 6), (1, 7), (1, 8), (2, 3), (2, 4), (2, 5)]
+        )
+        d = nx.group_degree_centrality(G, [1, 2])
+        d_answer = 1
+        assert d == d_answer
+
+    def test_group_in_degree_centrality(self):
+        """
+        Group in-degree centrality in a DiGraph
+        """
+        G = nx.DiGraph()
+        G.add_nodes_from([1, 2, 3, 4, 5, 6, 7, 8])
+        G.add_edges_from(
+            [(1, 2), (1, 3), (1, 6), (1, 7), (1, 8), (2, 3), (2, 4), (2, 5)]
+        )
+        d = nx.group_in_degree_centrality(G, [1, 2])
+        d_answer = 0
+        assert d == d_answer
+
+    def test_group_out_degree_centrality(self):
+        """
+        Group out-degree centrality in a DiGraph
+        """
+        G = nx.DiGraph()
+        G.add_nodes_from([1, 2, 3, 4, 5, 6, 7, 8])
+        G.add_edges_from(
+            [(1, 2), (1, 3), (1, 6), (1, 7), (1, 8), (2, 3), (2, 4), (2, 5)]
+        )
+        d = nx.group_out_degree_centrality(G, [1, 2])
+        d_answer = 1
+        assert d == d_answer
+
+    def test_group_degree_centrality_node_not_in_graph(self):
+        """
+        Node(s) in S not in graph, raises NetworkXError
+        """
+        with pytest.raises(nx.NetworkXError):
+            nx.group_degree_centrality(nx.path_graph(5), [6, 7, 8])

pythonProject/.venv/Lib/site-packages/networkx/algorithms/centrality/tests/test_harmonic_centrality.py

@@ -0,0 +1,115 @@
+"""
+Tests for degree centrality.
+"""
+import pytest
+
+import networkx as nx
+from networkx.algorithms.centrality import harmonic_centrality
+
+
+class TestClosenessCentrality:
+    @classmethod
+    def setup_class(cls):
+        cls.P3 = nx.path_graph(3)
+        cls.P4 = nx.path_graph(4)
+        cls.K5 = nx.complete_graph(5)
+
+        cls.C4 = nx.cycle_graph(4)
+        cls.C4_directed = nx.cycle_graph(4, create_using=nx.DiGraph)
+
+        cls.C5 = nx.cycle_graph(5)
+
+        cls.T = nx.balanced_tree(r=2, h=2)
+
+        cls.Gb = nx.DiGraph()
+        cls.Gb.add_edges_from([(0, 1), (0, 2), (0, 4), (2, 1), (2, 3), (4, 3)])
+
+    def test_p3_harmonic(self):
+        c = harmonic_centrality(self.P3)
+        d = {0: 1.5, 1: 2, 2: 1.5}
+        for n in sorted(self.P3):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_p4_harmonic(self):
+        c = harmonic_centrality(self.P4)
+        d = {0: 1.8333333, 1: 2.5, 2: 2.5, 3: 1.8333333}
+        for n in sorted(self.P4):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_clique_complete(self):
+        c = harmonic_centrality(self.K5)
+        d = {0: 4, 1: 4, 2: 4, 3: 4, 4: 4}
+        for n in sorted(self.P3):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_cycle_C4(self):
+        c = harmonic_centrality(self.C4)
+        d = {0: 2.5, 1: 2.5, 2: 2.5, 3: 2.5}
+        for n in sorted(self.C4):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_cycle_C5(self):
+        c = harmonic_centrality(self.C5)
+        d = {0: 3, 1: 3, 2: 3, 3: 3, 4: 3, 5: 4}
+        for n in sorted(self.C5):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_bal_tree(self):
+        c = harmonic_centrality(self.T)
+        d = {0: 4.0, 1: 4.1666, 2: 4.1666, 3: 2.8333, 4: 2.8333, 5: 2.8333, 6: 2.8333}
+        for n in sorted(self.T):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_exampleGraph(self):
+        c = harmonic_centrality(self.Gb)
+        d = {0: 0, 1: 2, 2: 1, 3: 2.5, 4: 1}
+        for n in sorted(self.Gb):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_weighted_harmonic(self):
+        XG = nx.DiGraph()
+        XG.add_weighted_edges_from(
+            [
+                ("a", "b", 10),
+                ("d", "c", 5),
+                ("a", "c", 1),
+                ("e", "f", 2),
+                ("f", "c", 1),
+                ("a", "f", 3),
+            ]
+        )
+        c = harmonic_centrality(XG, distance="weight")
+        d = {"a": 0, "b": 0.1, "c": 2.533, "d": 0, "e": 0, "f": 0.83333}
+        for n in sorted(XG):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_empty(self):
+        G = nx.DiGraph()
+        c = harmonic_centrality(G, distance="weight")
+        d = {}
+        assert c == d
+
+    def test_singleton(self):
+        G = nx.DiGraph()
+        G.add_node(0)
+        c = harmonic_centrality(G, distance="weight")
+        d = {0: 0}
+        assert c == d
+
+    def test_cycle_c4_directed(self):
+        c = harmonic_centrality(self.C4_directed, nbunch=[0, 1], sources=[1, 2])
+        d = {0: 0.833, 1: 0.333}
+        for n in [0, 1]:
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_p3_harmonic_subset(self):
+        c = harmonic_centrality(self.P3, sources=[0, 1])
+        d = {0: 1, 1: 1, 2: 1.5}
+        for n in self.P3:
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_p4_harmonic_subset(self):
+        c = harmonic_centrality(self.P4, nbunch=[2, 3], sources=[0, 1])
+        d = {2: 1.5, 3: 0.8333333}
+        for n in [2, 3]:
+            assert c[n] == pytest.approx(d[n], abs=1e-3)

pythonProject/.venv/Lib/site-packages/networkx/algorithms/centrality/tests/test_katz_centrality.py

@@ -0,0 +1,345 @@
+import math
+
+import pytest
+
+import networkx as nx
+
+
+class TestKatzCentrality:
+    def test_K5(self):
+        """Katz centrality: K5"""
+        G = nx.complete_graph(5)
+        alpha = 0.1
+        b = nx.katz_centrality(G, alpha)
+        v = math.sqrt(1 / 5.0)
+        b_answer = dict.fromkeys(G, v)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+        nstart = {n: 1 for n in G}
+        b = nx.katz_centrality(G, alpha, nstart=nstart)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_P3(self):
+        """Katz centrality: P3"""
+        alpha = 0.1
+        G = nx.path_graph(3)
+        b_answer = {0: 0.5598852584152165, 1: 0.6107839182711449, 2: 0.5598852584152162}
+        b = nx.katz_centrality(G, alpha)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-4)
+
+    def test_maxiter(self):
+        with pytest.raises(nx.PowerIterationFailedConvergence):
+            nx.katz_centrality(nx.path_graph(3), 0.1, max_iter=0)
+
+    def test_beta_as_scalar(self):
+        alpha = 0.1
+        beta = 0.1
+        b_answer = {0: 0.5598852584152165, 1: 0.6107839182711449, 2: 0.5598852584152162}
+        G = nx.path_graph(3)
+        b = nx.katz_centrality(G, alpha, beta)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-4)
+
+    def test_beta_as_dict(self):
+        alpha = 0.1
+        beta = {0: 1.0, 1: 1.0, 2: 1.0}
+        b_answer = {0: 0.5598852584152165, 1: 0.6107839182711449, 2: 0.5598852584152162}
+        G = nx.path_graph(3)
+        b = nx.katz_centrality(G, alpha, beta)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-4)
+
+    def test_multiple_alpha(self):
+        alpha_list = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6]
+        for alpha in alpha_list:
+            b_answer = {
+                0.1: {
+                    0: 0.5598852584152165,
+                    1: 0.6107839182711449,
+                    2: 0.5598852584152162,
+                },
+                0.2: {
+                    0: 0.5454545454545454,
+                    1: 0.6363636363636365,
+                    2: 0.5454545454545454,
+                },
+                0.3: {
+                    0: 0.5333964609104419,
+                    1: 0.6564879518897746,
+                    2: 0.5333964609104419,
+                },
+                0.4: {
+                    0: 0.5232045649263551,
+                    1: 0.6726915834767423,
+                    2: 0.5232045649263551,
+                },
+                0.5: {
+                    0: 0.5144957746691622,
+                    1: 0.6859943117075809,
+                    2: 0.5144957746691622,
+                },
+                0.6: {
+                    0: 0.5069794004195823,
+                    1: 0.6970966755769258,
+                    2: 0.5069794004195823,
+                },
+            }
+            G = nx.path_graph(3)
+            b = nx.katz_centrality(G, alpha)
+            for n in sorted(G):
+                assert b[n] == pytest.approx(b_answer[alpha][n], abs=1e-4)
+
+    def test_multigraph(self):
+        with pytest.raises(nx.NetworkXException):
+            nx.katz_centrality(nx.MultiGraph(), 0.1)
+
+    def test_empty(self):
+        e = nx.katz_centrality(nx.Graph(), 0.1)
+        assert e == {}
+
+    def test_bad_beta(self):
+        with pytest.raises(nx.NetworkXException):
+            G = nx.Graph([(0, 1)])
+            beta = {0: 77}
+            nx.katz_centrality(G, 0.1, beta=beta)
+
+    def test_bad_beta_number(self):
+        with pytest.raises(nx.NetworkXException):
+            G = nx.Graph([(0, 1)])
+            nx.katz_centrality(G, 0.1, beta="foo")
+
+
+class TestKatzCentralityNumpy:
+    @classmethod
+    def setup_class(cls):
+        global np
+        np = pytest.importorskip("numpy")
+        pytest.importorskip("scipy")
+
+    def test_K5(self):
+        """Katz centrality: K5"""
+        G = nx.complete_graph(5)
+        alpha = 0.1
+        b = nx.katz_centrality(G, alpha)
+        v = math.sqrt(1 / 5.0)
+        b_answer = dict.fromkeys(G, v)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+        b = nx.eigenvector_centrality_numpy(G)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-3)
+
+    def test_P3(self):
+        """Katz centrality: P3"""
+        alpha = 0.1
+        G = nx.path_graph(3)
+        b_answer = {0: 0.5598852584152165, 1: 0.6107839182711449, 2: 0.5598852584152162}
+        b = nx.katz_centrality_numpy(G, alpha)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-4)
+
+    def test_beta_as_scalar(self):
+        alpha = 0.1
+        beta = 0.1
+        b_answer = {0: 0.5598852584152165, 1: 0.6107839182711449, 2: 0.5598852584152162}
+        G = nx.path_graph(3)
+        b = nx.katz_centrality_numpy(G, alpha, beta)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-4)
+
+    def test_beta_as_dict(self):
+        alpha = 0.1
+        beta = {0: 1.0, 1: 1.0, 2: 1.0}
+        b_answer = {0: 0.5598852584152165, 1: 0.6107839182711449, 2: 0.5598852584152162}
+        G = nx.path_graph(3)
+        b = nx.katz_centrality_numpy(G, alpha, beta)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-4)
+
+    def test_multiple_alpha(self):
+        alpha_list = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6]
+        for alpha in alpha_list:
+            b_answer = {
+                0.1: {
+                    0: 0.5598852584152165,
+                    1: 0.6107839182711449,
+                    2: 0.5598852584152162,
+                },
+                0.2: {
+                    0: 0.5454545454545454,
+                    1: 0.6363636363636365,
+                    2: 0.5454545454545454,
+                },
+                0.3: {
+                    0: 0.5333964609104419,
+                    1: 0.6564879518897746,
+                    2: 0.5333964609104419,
+                },
+                0.4: {
+                    0: 0.5232045649263551,
+                    1: 0.6726915834767423,
+                    2: 0.5232045649263551,
+                },
+                0.5: {
+                    0: 0.5144957746691622,
+                    1: 0.6859943117075809,
+                    2: 0.5144957746691622,
+                },
+                0.6: {
+                    0: 0.5069794004195823,
+                    1: 0.6970966755769258,
+                    2: 0.5069794004195823,
+                },
+            }
+            G = nx.path_graph(3)
+            b = nx.katz_centrality_numpy(G, alpha)
+            for n in sorted(G):
+                assert b[n] == pytest.approx(b_answer[alpha][n], abs=1e-4)
+
+    def test_multigraph(self):
+        with pytest.raises(nx.NetworkXException):
+            nx.katz_centrality(nx.MultiGraph(), 0.1)
+
+    def test_empty(self):
+        e = nx.katz_centrality(nx.Graph(), 0.1)
+        assert e == {}
+
+    def test_bad_beta(self):
+        with pytest.raises(nx.NetworkXException):
+            G = nx.Graph([(0, 1)])
+            beta = {0: 77}
+            nx.katz_centrality_numpy(G, 0.1, beta=beta)
+
+    def test_bad_beta_numbe(self):
+        with pytest.raises(nx.NetworkXException):
+            G = nx.Graph([(0, 1)])
+            nx.katz_centrality_numpy(G, 0.1, beta="foo")
+
+    def test_K5_unweighted(self):
+        """Katz centrality: K5"""
+        G = nx.complete_graph(5)
+        alpha = 0.1
+        b = nx.katz_centrality(G, alpha, weight=None)
+        v = math.sqrt(1 / 5.0)
+        b_answer = dict.fromkeys(G, v)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+        b = nx.eigenvector_centrality_numpy(G, weight=None)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-3)
+
+    def test_P3_unweighted(self):
+        """Katz centrality: P3"""
+        alpha = 0.1
+        G = nx.path_graph(3)
+        b_answer = {0: 0.5598852584152165, 1: 0.6107839182711449, 2: 0.5598852584152162}
+        b = nx.katz_centrality_numpy(G, alpha, weight=None)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-4)
+
+
+class TestKatzCentralityDirected:
+    @classmethod
+    def setup_class(cls):
+        G = nx.DiGraph()
+        edges = [
+            (1, 2),
+            (1, 3),
+            (2, 4),
+            (3, 2),
+            (3, 5),
+            (4, 2),
+            (4, 5),
+            (4, 6),
+            (5, 6),
+            (5, 7),
+            (5, 8),
+            (6, 8),
+            (7, 1),
+            (7, 5),
+            (7, 8),
+            (8, 6),
+            (8, 7),
+        ]
+        G.add_edges_from(edges, weight=2.0)
+        cls.G = G.reverse()
+        cls.G.alpha = 0.1
+        cls.G.evc = [
+            0.3289589783189635,
+            0.2832077296243516,
+            0.3425906003685471,
+            0.3970420865198392,
+            0.41074871061646284,
+            0.272257430756461,
+            0.4201989685435462,
+            0.34229059218038554,
+        ]
+
+        H = nx.DiGraph(edges)
+        cls.H = G.reverse()
+        cls.H.alpha = 0.1
+        cls.H.evc = [
+            0.3289589783189635,
+            0.2832077296243516,
+            0.3425906003685471,
+            0.3970420865198392,
+            0.41074871061646284,
+            0.272257430756461,
+            0.4201989685435462,
+            0.34229059218038554,
+        ]
+
+    def test_katz_centrality_weighted(self):
+        G = self.G
+        alpha = self.G.alpha
+        p = nx.katz_centrality(G, alpha, weight="weight")
+        for a, b in zip(list(p.values()), self.G.evc):
+            assert a == pytest.approx(b, abs=1e-7)
+
+    def test_katz_centrality_unweighted(self):
+        H = self.H
+        alpha = self.H.alpha
+        p = nx.katz_centrality(H, alpha, weight="weight")
+        for a, b in zip(list(p.values()), self.H.evc):
+            assert a == pytest.approx(b, abs=1e-7)
+
+
+class TestKatzCentralityDirectedNumpy(TestKatzCentralityDirected):
+    @classmethod
+    def setup_class(cls):
+        global np
+        np = pytest.importorskip("numpy")
+        pytest.importorskip("scipy")
+        super().setup_class()
+
+    def test_katz_centrality_weighted(self):
+        G = self.G
+        alpha = self.G.alpha
+        p = nx.katz_centrality_numpy(G, alpha, weight="weight")
+        for a, b in zip(list(p.values()), self.G.evc):
+            assert a == pytest.approx(b, abs=1e-7)
+
+    def test_katz_centrality_unweighted(self):
+        H = self.H
+        alpha = self.H.alpha
+        p = nx.katz_centrality_numpy(H, alpha, weight="weight")
+        for a, b in zip(list(p.values()), self.H.evc):
+            assert a == pytest.approx(b, abs=1e-7)
+
+
+class TestKatzEigenvectorVKatz:
+    @classmethod
+    def setup_class(cls):
+        global np
+        np = pytest.importorskip("numpy")
+        pytest.importorskip("scipy")
+
+    def test_eigenvector_v_katz_random(self):
+        G = nx.gnp_random_graph(10, 0.5, seed=1234)
+        l = max(np.linalg.eigvals(nx.adjacency_matrix(G).todense()))
+        e = nx.eigenvector_centrality_numpy(G)
+        k = nx.katz_centrality_numpy(G, 1.0 / l)
+        for n in G:
+            assert e[n] == pytest.approx(k[n], abs=1e-7)

pythonProject/.venv/Lib/site-packages/networkx/algorithms/centrality/tests/test_laplacian_centrality.py

@@ -0,0 +1,221 @@
+import pytest
+
+import networkx as nx
+
+np = pytest.importorskip("numpy")
+sp = pytest.importorskip("scipy")
+
+
+def test_laplacian_centrality_null_graph():
+    G = nx.Graph()
+    with pytest.raises(nx.NetworkXPointlessConcept):
+        d = nx.laplacian_centrality(G, normalized=False)
+
+
+def test_laplacian_centrality_single_node():
+    """See gh-6571"""
+    G = nx.empty_graph(1)
+    assert nx.laplacian_centrality(G, normalized=False) == {0: 0}
+    with pytest.raises(ZeroDivisionError):
+        nx.laplacian_centrality(G, normalized=True)
+
+
+def test_laplacian_centrality_unconnected_nodes():
+    """laplacian_centrality on a unconnected node graph should return 0
+
+    For graphs without edges, the Laplacian energy is 0 and is unchanged with
+    node removal, so::
+
+        LC(v) = LE(G) - LE(G - v) = 0 - 0 = 0
+    """
+    G = nx.empty_graph(3)
+    assert nx.laplacian_centrality(G, normalized=False) == {0: 0, 1: 0, 2: 0}
+
+
+def test_laplacian_centrality_empty_graph():
+    G = nx.empty_graph(3)
+    with pytest.raises(ZeroDivisionError):
+        d = nx.laplacian_centrality(G, normalized=True)
+
+
+def test_laplacian_centrality_E():
+    E = nx.Graph()
+    E.add_weighted_edges_from(
+        [(0, 1, 4), (4, 5, 1), (0, 2, 2), (2, 1, 1), (1, 3, 2), (1, 4, 2)]
+    )
+    d = nx.laplacian_centrality(E)
+    exact = {
+        0: 0.700000,
+        1: 0.900000,
+        2: 0.280000,
+        3: 0.220000,
+        4: 0.260000,
+        5: 0.040000,
+    }
+
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+    # Check not normalized
+    full_energy = 200
+    dnn = nx.laplacian_centrality(E, normalized=False)
+    for n, dc in dnn.items():
+        assert exact[n] * full_energy == pytest.approx(dc, abs=1e-7)
+
+    # Check unweighted not-normalized version
+    duw_nn = nx.laplacian_centrality(E, normalized=False, weight=None)
+    print(duw_nn)
+    exact_uw_nn = {
+        0: 18,
+        1: 34,
+        2: 18,
+        3: 10,
+        4: 16,
+        5: 6,
+    }
+    for n, dc in duw_nn.items():
+        assert exact_uw_nn[n] == pytest.approx(dc, abs=1e-7)
+
+    # Check unweighted version
+    duw = nx.laplacian_centrality(E, weight=None)
+    full_energy = 42
+    for n, dc in duw.items():
+        assert exact_uw_nn[n] / full_energy == pytest.approx(dc, abs=1e-7)
+
+
+def test_laplacian_centrality_KC():
+    KC = nx.karate_club_graph()
+    d = nx.laplacian_centrality(KC)
+    exact = {
+        0: 0.2543593,
+        1: 0.1724524,
+        2: 0.2166053,
+        3: 0.0964646,
+        4: 0.0350344,
+        5: 0.0571109,
+        6: 0.0540713,
+        7: 0.0788674,
+        8: 0.1222204,
+        9: 0.0217565,
+        10: 0.0308751,
+        11: 0.0215965,
+        12: 0.0174372,
+        13: 0.118861,
+        14: 0.0366341,
+        15: 0.0548712,
+        16: 0.0172772,
+        17: 0.0191969,
+        18: 0.0225564,
+        19: 0.0331147,
+        20: 0.0279955,
+        21: 0.0246361,
+        22: 0.0382339,
+        23: 0.1294193,
+        24: 0.0227164,
+        25: 0.0644697,
+        26: 0.0281555,
+        27: 0.075188,
+        28: 0.0364742,
+        29: 0.0707087,
+        30: 0.0708687,
+        31: 0.131019,
+        32: 0.2370821,
+        33: 0.3066709,
+    }
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+    # Check not normalized
+    full_energy = 12502
+    dnn = nx.laplacian_centrality(KC, normalized=False)
+    for n, dc in dnn.items():
+        assert exact[n] * full_energy == pytest.approx(dc, abs=1e-3)
+
+
+def test_laplacian_centrality_K():
+    K = nx.krackhardt_kite_graph()
+    d = nx.laplacian_centrality(K)
+    exact = {
+        0: 0.3010753,
+        1: 0.3010753,
+        2: 0.2258065,
+        3: 0.483871,
+        4: 0.2258065,
+        5: 0.3870968,
+        6: 0.3870968,
+        7: 0.1935484,
+        8: 0.0752688,
+        9: 0.0322581,
+    }
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+    # Check not normalized
+    full_energy = 186
+    dnn = nx.laplacian_centrality(K, normalized=False)
+    for n, dc in dnn.items():
+        assert exact[n] * full_energy == pytest.approx(dc, abs=1e-3)
+
+
+def test_laplacian_centrality_P3():
+    P3 = nx.path_graph(3)
+    d = nx.laplacian_centrality(P3)
+    exact = {0: 0.6, 1: 1.0, 2: 0.6}
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+
+def test_laplacian_centrality_K5():
+    K5 = nx.complete_graph(5)
+    d = nx.laplacian_centrality(K5)
+    exact = {0: 0.52, 1: 0.52, 2: 0.52, 3: 0.52, 4: 0.52}
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+
+def test_laplacian_centrality_FF():
+    FF = nx.florentine_families_graph()
+    d = nx.laplacian_centrality(FF)
+    exact = {
+        "Acciaiuoli": 0.0804598,
+        "Medici": 0.4022989,
+        "Castellani": 0.1724138,
+        "Peruzzi": 0.183908,
+        "Strozzi": 0.2528736,
+        "Barbadori": 0.137931,
+        "Ridolfi": 0.2183908,
+        "Tornabuoni": 0.2183908,
+        "Albizzi": 0.1954023,
+        "Salviati": 0.1149425,
+        "Pazzi": 0.0344828,
+        "Bischeri": 0.1954023,
+        "Guadagni": 0.2298851,
+        "Ginori": 0.045977,
+        "Lamberteschi": 0.0574713,
+    }
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+
+def test_laplacian_centrality_DG():
+    DG = nx.DiGraph([(0, 5), (1, 5), (2, 5), (3, 5), (4, 5), (5, 6), (5, 7), (5, 8)])
+    d = nx.laplacian_centrality(DG)
+    exact = {
+        0: 0.2123352,
+        5: 0.515391,
+        1: 0.2123352,
+        2: 0.2123352,
+        3: 0.2123352,
+        4: 0.2123352,
+        6: 0.2952031,
+        7: 0.2952031,
+        8: 0.2952031,
+    }
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+    # Check not normalized
+    full_energy = 9.50704
+    dnn = nx.laplacian_centrality(DG, normalized=False)
+    for n, dc in dnn.items():
+        assert exact[n] * full_energy == pytest.approx(dc, abs=1e-4)