#!/usr/bin/env python 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. / 12, 1: 1. / 4, 2: 1. / 12, 3: 1. / 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)