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#!/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)
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