File: //lib/python3/dist-packages/networkx/algorithms/centrality/tests/test_load_centrality.py
#!/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)