view env/lib/python3.9/site-packages/networkx/algorithms/centrality/tests/test_load_centrality.py @ 0:4f3585e2f14b draft default tip

"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"

import networkx as nx
from networkx.testing import almost_equal


class TestLoadCentrality:
    @classmethod
    def setup_class(cls):

        G = nx.Graph()
        G.add_edge(0, 1, weight=3)
        G.add_edge(0, 2, weight=2)
        G.add_edge(0, 3, weight=6)
        G.add_edge(0, 4, weight=4)
        G.add_edge(1, 3, weight=5)
        G.add_edge(1, 5, weight=5)
        G.add_edge(2, 4, weight=1)
        G.add_edge(3, 4, weight=2)
        G.add_edge(3, 5, weight=1)
        G.add_edge(4, 5, weight=4)
        cls.G = G
        cls.exact_weighted = {0: 4.0, 1: 0.0, 2: 8.0, 3: 6.0, 4: 8.0, 5: 0.0}
        cls.K = nx.krackhardt_kite_graph()
        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.T = nx.balanced_tree(r=2, h=2)
        cls.Gb = nx.Graph()
        cls.Gb.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3), (2, 4), (4, 5), (3, 5)])
        cls.F = nx.florentine_families_graph()
        cls.LM = nx.les_miserables_graph()
        cls.D = nx.cycle_graph(3, create_using=nx.DiGraph())
        cls.D.add_edges_from([(3, 0), (4, 3)])

    def test_not_strongly_connected(self):
        b = nx.load_centrality(self.D)
        result = {0: 5.0 / 12, 1: 1.0 / 4, 2: 1.0 / 12, 3: 1.0 / 4, 4: 0.000}
        for n in sorted(self.D):
            assert almost_equal(result[n], b[n], places=3)
            assert almost_equal(result[n], nx.load_centrality(self.D, n), places=3)

    def test_weighted_load(self):
        b = nx.load_centrality(self.G, weight="weight", normalized=False)
        for n in sorted(self.G):
            assert b[n] == self.exact_weighted[n]

    def test_k5_load(self):
        G = self.K5
        c = nx.load_centrality(G)
        d = {0: 0.000, 1: 0.000, 2: 0.000, 3: 0.000, 4: 0.000}
        for n in sorted(G):
            assert almost_equal(c[n], d[n], places=3)

    def test_p3_load(self):
        G = self.P3
        c = nx.load_centrality(G)
        d = {0: 0.000, 1: 1.000, 2: 0.000}
        for n in sorted(G):
            assert almost_equal(c[n], d[n], places=3)
        c = nx.load_centrality(G, v=1)
        assert almost_equal(c, 1.0)
        c = nx.load_centrality(G, v=1, normalized=True)
        assert almost_equal(c, 1.0)

    def test_p2_load(self):
        G = nx.path_graph(2)
        c = nx.load_centrality(G)
        d = {0: 0.000, 1: 0.000}
        for n in sorted(G):
            assert almost_equal(c[n], d[n], places=3)

    def test_krackhardt_load(self):
        G = self.K
        c = nx.load_centrality(G)
        d = {
            0: 0.023,
            1: 0.023,
            2: 0.000,
            3: 0.102,
            4: 0.000,
            5: 0.231,
            6: 0.231,
            7: 0.389,
            8: 0.222,
            9: 0.000,
        }
        for n in sorted(G):
            assert almost_equal(c[n], d[n], places=3)

    def test_florentine_families_load(self):
        G = self.F
        c = nx.load_centrality(G)
        d = {
            "Acciaiuoli": 0.000,
            "Albizzi": 0.211,
            "Barbadori": 0.093,
            "Bischeri": 0.104,
            "Castellani": 0.055,
            "Ginori": 0.000,
            "Guadagni": 0.251,
            "Lamberteschi": 0.000,
            "Medici": 0.522,
            "Pazzi": 0.000,
            "Peruzzi": 0.022,
            "Ridolfi": 0.117,
            "Salviati": 0.143,
            "Strozzi": 0.106,
            "Tornabuoni": 0.090,
        }
        for n in sorted(G):
            assert almost_equal(c[n], d[n], places=3)

    def test_les_miserables_load(self):
        G = self.LM
        c = nx.load_centrality(G)
        d = {
            "Napoleon": 0.000,
            "Myriel": 0.177,
            "MlleBaptistine": 0.000,
            "MmeMagloire": 0.000,
            "CountessDeLo": 0.000,
            "Geborand": 0.000,
            "Champtercier": 0.000,
            "Cravatte": 0.000,
            "Count": 0.000,
            "OldMan": 0.000,
            "Valjean": 0.567,
            "Labarre": 0.000,
            "Marguerite": 0.000,
            "MmeDeR": 0.000,
            "Isabeau": 0.000,
            "Gervais": 0.000,
            "Listolier": 0.000,
            "Tholomyes": 0.043,
            "Fameuil": 0.000,
            "Blacheville": 0.000,
            "Favourite": 0.000,
            "Dahlia": 0.000,
            "Zephine": 0.000,
            "Fantine": 0.128,
            "MmeThenardier": 0.029,
            "Thenardier": 0.075,
            "Cosette": 0.024,
            "Javert": 0.054,
            "Fauchelevent": 0.026,
            "Bamatabois": 0.008,
            "Perpetue": 0.000,
            "Simplice": 0.009,
            "Scaufflaire": 0.000,
            "Woman1": 0.000,
            "Judge": 0.000,
            "Champmathieu": 0.000,
            "Brevet": 0.000,
            "Chenildieu": 0.000,
            "Cochepaille": 0.000,
            "Pontmercy": 0.007,
            "Boulatruelle": 0.000,
            "Eponine": 0.012,
            "Anzelma": 0.000,
            "Woman2": 0.000,
            "MotherInnocent": 0.000,
            "Gribier": 0.000,
            "MmeBurgon": 0.026,
            "Jondrette": 0.000,
            "Gavroche": 0.164,
            "Gillenormand": 0.021,
            "Magnon": 0.000,
            "MlleGillenormand": 0.047,
            "MmePontmercy": 0.000,
            "MlleVaubois": 0.000,
            "LtGillenormand": 0.000,
            "Marius": 0.133,
            "BaronessT": 0.000,
            "Mabeuf": 0.028,
            "Enjolras": 0.041,
            "Combeferre": 0.001,
            "Prouvaire": 0.000,
            "Feuilly": 0.001,
            "Courfeyrac": 0.006,
            "Bahorel": 0.002,
            "Bossuet": 0.032,
            "Joly": 0.002,
            "Grantaire": 0.000,
            "MotherPlutarch": 0.000,
            "Gueulemer": 0.005,
            "Babet": 0.005,
            "Claquesous": 0.005,
            "Montparnasse": 0.004,
            "Toussaint": 0.000,
            "Child1": 0.000,
            "Child2": 0.000,
            "Brujon": 0.000,
            "MmeHucheloup": 0.000,
        }
        for n in sorted(G):
            assert almost_equal(c[n], d[n], places=3)

    def test_unnormalized_k5_load(self):
        G = self.K5
        c = nx.load_centrality(G, normalized=False)
        d = {0: 0.000, 1: 0.000, 2: 0.000, 3: 0.000, 4: 0.000}
        for n in sorted(G):
            assert almost_equal(c[n], d[n], places=3)

    def test_unnormalized_p3_load(self):
        G = self.P3
        c = nx.load_centrality(G, normalized=False)
        d = {0: 0.000, 1: 2.000, 2: 0.000}
        for n in sorted(G):
            assert almost_equal(c[n], d[n], places=3)

    def test_unnormalized_krackhardt_load(self):
        G = self.K
        c = nx.load_centrality(G, normalized=False)
        d = {
            0: 1.667,
            1: 1.667,
            2: 0.000,
            3: 7.333,
            4: 0.000,
            5: 16.667,
            6: 16.667,
            7: 28.000,
            8: 16.000,
            9: 0.000,
        }

        for n in sorted(G):
            assert almost_equal(c[n], d[n], places=3)

    def test_unnormalized_florentine_families_load(self):
        G = self.F
        c = nx.load_centrality(G, normalized=False)

        d = {
            "Acciaiuoli": 0.000,
            "Albizzi": 38.333,
            "Barbadori": 17.000,
            "Bischeri": 19.000,
            "Castellani": 10.000,
            "Ginori": 0.000,
            "Guadagni": 45.667,
            "Lamberteschi": 0.000,
            "Medici": 95.000,
            "Pazzi": 0.000,
            "Peruzzi": 4.000,
            "Ridolfi": 21.333,
            "Salviati": 26.000,
            "Strozzi": 19.333,
            "Tornabuoni": 16.333,
        }
        for n in sorted(G):
            assert almost_equal(c[n], d[n], places=3)

    def test_load_betweenness_difference(self):
        # Difference Between Load and Betweenness
        # --------------------------------------- The smallest graph
        # that shows the difference between load and betweenness is
        # G=ladder_graph(3) (Graph B below)

        # Graph A and B are from Tao Zhou, Jian-Guo Liu, Bing-Hong
        # Wang: Comment on "Scientific collaboration
        # networks. II. Shortest paths, weighted networks, and
        # centrality". https://arxiv.org/pdf/physics/0511084

        # Notice that unlike here, their calculation adds to 1 to the
        # betweennes of every node i for every path from i to every
        # other node.  This is exactly what it should be, based on
        # Eqn. (1) in their paper: the eqn is B(v) = \sum_{s\neq t,
        # s\neq v}{\frac{\sigma_{st}(v)}{\sigma_{st}}}, therefore,
        # they allow v to be the target node.

        # We follow Brandes 2001, who follows Freeman 1977 that make
        # the sum for betweenness of v exclude paths where v is either
        # the source or target node.  To agree with their numbers, we
        # must additionally, remove edge (4,8) from the graph, see AC
        # example following (there is a mistake in the figure in their
        # paper - personal communication).

        # A = nx.Graph()
        # A.add_edges_from([(0,1), (1,2), (1,3), (2,4),
        #                  (3,5), (4,6), (4,7), (4,8),
        #                  (5,8), (6,9), (7,9), (8,9)])
        B = nx.Graph()  # ladder_graph(3)
        B.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3), (2, 4), (4, 5), (3, 5)])
        c = nx.load_centrality(B, normalized=False)
        d = {0: 1.750, 1: 1.750, 2: 6.500, 3: 6.500, 4: 1.750, 5: 1.750}
        for n in sorted(B):
            assert almost_equal(c[n], d[n], places=3)

    def test_c4_edge_load(self):
        G = self.C4
        c = nx.edge_load_centrality(G)
        d = {(0, 1): 6.000, (0, 3): 6.000, (1, 2): 6.000, (2, 3): 6.000}
        for n in G.edges():
            assert almost_equal(c[n], d[n], places=3)

    def test_p4_edge_load(self):
        G = self.P4
        c = nx.edge_load_centrality(G)
        d = {(0, 1): 6.000, (1, 2): 8.000, (2, 3): 6.000}
        for n in G.edges():
            assert almost_equal(c[n], d[n], places=3)

    def test_k5_edge_load(self):
        G = self.K5
        c = nx.edge_load_centrality(G)
        d = {
            (0, 1): 5.000,
            (0, 2): 5.000,
            (0, 3): 5.000,
            (0, 4): 5.000,
            (1, 2): 5.000,
            (1, 3): 5.000,
            (1, 4): 5.000,
            (2, 3): 5.000,
            (2, 4): 5.000,
            (3, 4): 5.000,
        }
        for n in G.edges():
            assert almost_equal(c[n], d[n], places=3)

    def test_tree_edge_load(self):
        G = self.T
        c = nx.edge_load_centrality(G)
        d = {
            (0, 1): 24.000,
            (0, 2): 24.000,
            (1, 3): 12.000,
            (1, 4): 12.000,
            (2, 5): 12.000,
            (2, 6): 12.000,
        }
        for n in G.edges():
            assert almost_equal(c[n], d[n], places=3)