#!/usr/bin/env python from nose.tools import * import networkx as nx class TestLoadCentrality: def setUp(self): 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) self.G=G self.exact_weighted={0: 4.0, 1: 0.0, 2: 8.0, 3: 6.0, 4: 8.0, 5: 0.0} self.K = nx.krackhardt_kite_graph() self.P3 = nx.path_graph(3) self.P4 = nx.path_graph(4) self.K5 = nx.complete_graph(5) self.C4=nx.cycle_graph(4) self.T=nx.balanced_tree(r=2, h=2) self.Gb = nx.Graph() self.Gb.add_edges_from([(0,1), (0,2), (1,3), (2,3), (2,4), (4,5), (3,5)]) F = nx.florentine_families_graph() self.F = F def test_weighted_load(self): b=nx.load_centrality(self.G,weight='weight',normalized=False) for n in sorted(self.G): assert_equal(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_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". http://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(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(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(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(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)