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#!/usr/bin/env python
from nose.tools import *
import networkx as nx
def weighted_G():
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)
return G
class TestBetweennessCentrality(object):
def test_K5(self):
"""Betweenness centrality: K5"""
G=nx.complete_graph(5)
b=nx.betweenness_centrality(G,
weight=None,
normalized=False)
b_answer={0: 0.0, 1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0}
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n])
def test_K5_endpoints(self):
"""Betweenness centrality: K5 endpoints"""
G=nx.complete_graph(5)
b=nx.betweenness_centrality(G,
weight=None,
normalized=False,
endpoints=True)
b_answer={0: 4.0, 1: 4.0, 2: 4.0, 3: 4.0, 4: 4.0}
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n])
def test_P3_normalized(self):
"""Betweenness centrality: P3 normalized"""
G=nx.path_graph(3)
b=nx.betweenness_centrality(G,
weight=None,
normalized=True)
b_answer={0: 0.0, 1: 1.0, 2: 0.0}
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n])
def test_P3(self):
"""Betweenness centrality: P3"""
G=nx.path_graph(3)
b_answer={0: 0.0, 1: 1.0, 2: 0.0}
b=nx.betweenness_centrality(G,
weight=None,
normalized=False)
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n])
def test_P3_endpoints(self):
"""Betweenness centrality: P3 endpoints"""
G=nx.path_graph(3)
b_answer={0: 2.0, 1: 3.0, 2: 2.0}
b=nx.betweenness_centrality(G,
weight=None,
normalized=False,
endpoints=True)
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n])
def test_krackhardt_kite_graph(self):
"""Betweenness centrality: Krackhardt kite graph"""
G=nx.krackhardt_kite_graph()
b_answer={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 b in b_answer:
b_answer[b]/=2.0
b=nx.betweenness_centrality(G,
weight=None,
normalized=False)
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n],places=3)
def test_krackhardt_kite_graph_normalized(self):
"""Betweenness centrality: Krackhardt kite graph normalized"""
G=nx.krackhardt_kite_graph()
b_answer={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}
b=nx.betweenness_centrality(G,
weight=None,
normalized=True)
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n],places=3)
def test_florentine_families_graph(self):
"""Betweenness centrality: Florentine families graph"""
G=nx.florentine_families_graph()
b_answer=\
{'Acciaiuoli': 0.000,
'Albizzi': 0.212,
'Barbadori': 0.093,
'Bischeri': 0.104,
'Castellani': 0.055,
'Ginori': 0.000,
'Guadagni': 0.255,
'Lamberteschi': 0.000,
'Medici': 0.522,
'Pazzi': 0.000,
'Peruzzi': 0.022,
'Ridolfi': 0.114,
'Salviati': 0.143,
'Strozzi': 0.103,
'Tornabuoni': 0.092}
b=nx.betweenness_centrality(G,
weight=None,
normalized=True)
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n],places=3)
def test_ladder_graph(self):
"""Betweenness centrality: Ladder graph"""
G = nx.Graph() # ladder_graph(3)
G.add_edges_from([(0,1), (0,2), (1,3), (2,3),
(2,4), (4,5), (3,5)])
b_answer={0:1.667,1: 1.667,2: 6.667,
3: 6.667,4: 1.667,5: 1.667}
for b in b_answer:
b_answer[b]/=2.0
b=nx.betweenness_centrality(G,
weight=None,
normalized=False)
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n],places=3)
def test_disconnected_path(self):
"""Betweenness centrality: disconnected path"""
G=nx.Graph()
G.add_path([0,1,2])
G.add_path([3,4,5,6])
b_answer={0:0,1:1,2:0,3:0,4:2,5:2,6:0}
b=nx.betweenness_centrality(G,
weight=None,
normalized=False)
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n])
def test_disconnected_path_endpoints(self):
"""Betweenness centrality: disconnected path endpoints"""
G=nx.Graph()
G.add_path([0,1,2])
G.add_path([3,4,5,6])
b_answer={0:2,1:3,2:2,3:3,4:5,5:5,6:3}
b=nx.betweenness_centrality(G,
weight=None,
normalized=False,
endpoints=True)
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n])
def test_directed_path(self):
"""Betweenness centrality: directed path"""
G=nx.DiGraph()
G.add_path([0,1,2])
b=nx.betweenness_centrality(G,
weight=None,
normalized=False)
b_answer={0: 0.0, 1: 1.0, 2: 0.0}
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n])
def test_directed_path_normalized(self):
"""Betweenness centrality: directed path normalized"""
G=nx.DiGraph()
G.add_path([0,1,2])
b=nx.betweenness_centrality(G,
weight=None,
normalized=True)
b_answer={0: 0.0, 1: 0.5, 2: 0.0}
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n])
class TestWeightedBetweennessCentrality(object):
def test_K5(self):
"""Weighted betweenness centrality: K5"""
G=nx.complete_graph(5)
b=nx.betweenness_centrality(G,
weight='weight',
normalized=False)
b_answer={0: 0.0, 1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0}
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n])
def test_P3_normalized(self):
"""Weighted betweenness centrality: P3 normalized"""
G=nx.path_graph(3)
b=nx.betweenness_centrality(G,
weight='weight',
normalized=True)
b_answer={0: 0.0, 1: 1.0, 2: 0.0}
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n])
def test_P3(self):
"""Weighted betweenness centrality: P3"""
G=nx.path_graph(3)
b_answer={0: 0.0, 1: 1.0, 2: 0.0}
b=nx.betweenness_centrality(G,
weight='weight',
normalized=False)
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n])
def test_krackhardt_kite_graph(self):
"""Weighted betweenness centrality: Krackhardt kite graph"""
G=nx.krackhardt_kite_graph()
b_answer={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 b in b_answer:
b_answer[b]/=2.0
b=nx.betweenness_centrality(G,
weight='weight',
normalized=False)
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n],places=3)
def test_krackhardt_kite_graph_normalized(self):
"""Weighted betweenness centrality:
Krackhardt kite graph normalized
"""
G=nx.krackhardt_kite_graph()
b_answer={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}
b=nx.betweenness_centrality(G,
weight='weight',
normalized=True)
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n],places=3)
def test_florentine_families_graph(self):
"""Weighted betweenness centrality:
Florentine families graph"""
G=nx.florentine_families_graph()
b_answer=\
{'Acciaiuoli': 0.000,
'Albizzi': 0.212,
'Barbadori': 0.093,
'Bischeri': 0.104,
'Castellani': 0.055,
'Ginori': 0.000,
'Guadagni': 0.255,
'Lamberteschi': 0.000,
'Medici': 0.522,
'Pazzi': 0.000,
'Peruzzi': 0.022,
'Ridolfi': 0.114,
'Salviati': 0.143,
'Strozzi': 0.103,
'Tornabuoni': 0.092}
b=nx.betweenness_centrality(G,
weight='weight',
normalized=True)
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n],places=3)
def test_ladder_graph(self):
"""Weighted betweenness centrality: Ladder graph"""
G = nx.Graph() # ladder_graph(3)
G.add_edges_from([(0,1), (0,2), (1,3), (2,3),
(2,4), (4,5), (3,5)])
b_answer={0:1.667,1: 1.667,2: 6.667,
3: 6.667,4: 1.667,5: 1.667}
for b in b_answer:
b_answer[b]/=2.0
b=nx.betweenness_centrality(G,
weight='weight',
normalized=False)
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n],places=3)
def test_G(self):
"""Weighted betweenness centrality: G"""
G = weighted_G()
b_answer={0: 2.0, 1: 0.0, 2: 4.0, 3: 3.0, 4: 4.0, 5: 0.0}
b=nx.betweenness_centrality(G,
weight='weight',
normalized=False)
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n])
def test_G2(self):
"""Weighted betweenness centrality: G2"""
G=nx.DiGraph()
G.add_weighted_edges_from([('s','u',10) ,('s','x',5) ,
('u','v',1) ,('u','x',2) ,
('v','y',1) ,('x','u',3) ,
('x','v',5) ,('x','y',2) ,
('y','s',7) ,('y','v',6)])
b_answer={'y':5.0,'x':5.0,'s':4.0,'u':2.0,'v':2.0}
b=nx.betweenness_centrality(G,
weight='weight',
normalized=False)
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n])
class TestEdgeBetweennessCentrality(object):
def test_K5(self):
"""Edge betweenness centrality: K5"""
G=nx.complete_graph(5)
b=nx.edge_betweenness_centrality(G, weight=None, normalized=False)
b_answer=dict.fromkeys(G.edges(),1)
for n in sorted(G.edges()):
assert_almost_equal(b[n],b_answer[n])
def test_normalized_K5(self):
"""Edge betweenness centrality: K5"""
G=nx.complete_graph(5)
b=nx.edge_betweenness_centrality(G, weight=None, normalized=True)
b_answer=dict.fromkeys(G.edges(),1/10.0)
for n in sorted(G.edges()):
assert_almost_equal(b[n],b_answer[n])
def test_C4(self):
"""Edge betweenness centrality: C4"""
G=nx.cycle_graph(4)
b=nx.edge_betweenness_centrality(G, weight=None, normalized=True)
b_answer={(0, 1):2,(0, 3):2, (1, 2):2, (2, 3): 2}
for n in sorted(G.edges()):
assert_almost_equal(b[n],b_answer[n]/6.0)
def test_P4(self):
"""Edge betweenness centrality: P4"""
G=nx.path_graph(4)
b=nx.edge_betweenness_centrality(G, weight=None, normalized=False)
b_answer={(0, 1):3,(1, 2):4, (2, 3):3}
for n in sorted(G.edges()):
assert_almost_equal(b[n],b_answer[n])
def test_normalized_P4(self):
"""Edge betweenness centrality: P4"""
G=nx.path_graph(4)
b=nx.edge_betweenness_centrality(G, weight=None, normalized=True)
b_answer={(0, 1):3,(1, 2):4, (2, 3):3}
for n in sorted(G.edges()):
assert_almost_equal(b[n],b_answer[n]/6.0)
def test_balanced_tree(self):
"""Edge betweenness centrality: balanced tree"""
G=nx.balanced_tree(r=2,h=2)
b=nx.edge_betweenness_centrality(G, weight=None, normalized=False)
b_answer={(0, 1):12,(0, 2):12,
(1, 3):6,(1, 4):6,(2, 5):6,(2,6):6}
for n in sorted(G.edges()):
assert_almost_equal(b[n],b_answer[n])
class TestWeightedEdgeBetweennessCentrality(object):
def test_K5(self):
"""Edge betweenness centrality: K5"""
G=nx.complete_graph(5)
b=nx.edge_betweenness_centrality(G, weight='weight', normalized=False)
b_answer=dict.fromkeys(G.edges(),1)
for n in sorted(G.edges()):
assert_almost_equal(b[n],b_answer[n])
def test_C4(self):
"""Edge betweenness centrality: C4"""
G=nx.cycle_graph(4)
b=nx.edge_betweenness_centrality(G, weight='weight', normalized=False)
b_answer={(0, 1):2,(0, 3):2, (1, 2):2, (2, 3): 2}
for n in sorted(G.edges()):
assert_almost_equal(b[n],b_answer[n])
def test_P4(self):
"""Edge betweenness centrality: P4"""
G=nx.path_graph(4)
b=nx.edge_betweenness_centrality(G, weight='weight', normalized=False)
b_answer={(0, 1):3,(1, 2):4, (2, 3):3}
for n in sorted(G.edges()):
assert_almost_equal(b[n],b_answer[n])
def test_balanced_tree(self):
"""Edge betweenness centrality: balanced tree"""
G=nx.balanced_tree(r=2,h=2)
b=nx.edge_betweenness_centrality(G, weight='weight', normalized=False)
b_answer={(0, 1):12,(0, 2):12,
(1, 3):6,(1, 4):6,(2, 5):6,(2,6):6}
for n in sorted(G.edges()):
assert_almost_equal(b[n],b_answer[n])
def test_weighted_graph(self):
eList = [(0, 1, 5), (0, 2, 4), (0, 3, 3),
(0, 4, 2), (1, 2, 4), (1, 3, 1),
(1, 4, 3), (2, 4, 5), (3, 4, 4)]
G = nx.Graph()
G.add_weighted_edges_from(eList)
b = nx.edge_betweenness_centrality(G, weight='weight', normalized=False)
b_answer={(0, 1):0.0,
(0, 2):1.0,
(0, 3):2.0,
(0, 4):1.0,
(1, 2):2.0,
(1, 3):3.5,
(1, 4):1.5,
(2, 4):1.0,
(3, 4):0.5}
for n in sorted(G.edges()):
assert_almost_equal(b[n],b_answer[n])
def test_normalized_weighted_graph(self):
eList = [(0, 1, 5), (0, 2, 4), (0, 3, 3),
(0, 4, 2), (1, 2, 4), (1, 3, 1),
(1, 4, 3), (2, 4, 5), (3, 4, 4)]
G = nx.Graph()
G.add_weighted_edges_from(eList)
b = nx.edge_betweenness_centrality(G, weight='weight', normalized=True)
b_answer={(0, 1):0.0,
(0, 2):1.0,
(0, 3):2.0,
(0, 4):1.0,
(1, 2):2.0,
(1, 3):3.5,
(1, 4):1.5,
(2, 4):1.0,
(3, 4):0.5}
norm = len(G)*(len(G)-1)/2.0
for n in sorted(G.edges()):
assert_almost_equal(b[n],b_answer[n]/norm)
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