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import pytest
import networkx as nx
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: 5.0 / 12, 1: 1.0 / 4, 2: 1.0 / 12, 3: 1.0 / 4, 4: 0.000}
for n in sorted(self.D):
assert result[n] == pytest.approx(b[n], abs=1e-3)
assert result[n] == pytest.approx(nx.load_centrality(self.D, n), abs=1e-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 c[n] == pytest.approx(d[n], abs=1e-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 c[n] == pytest.approx(d[n], abs=1e-3)
c = nx.load_centrality(G, v=1)
assert c == pytest.approx(1.0, abs=1e-7)
c = nx.load_centrality(G, v=1, normalized=True)
assert c == pytest.approx(1.0, abs=1e-7)
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 c[n] == pytest.approx(d[n], abs=1e-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 c[n] == pytest.approx(d[n], abs=1e-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 c[n] == pytest.approx(d[n], abs=1e-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 c[n] == pytest.approx(d[n], abs=1e-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 c[n] == pytest.approx(d[n], abs=1e-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 c[n] == pytest.approx(d[n], abs=1e-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 c[n] == pytest.approx(d[n], abs=1e-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 c[n] == pytest.approx(d[n], abs=1e-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 c[n] == pytest.approx(d[n], abs=1e-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 c[n] == pytest.approx(d[n], abs=1e-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 c[n] == pytest.approx(d[n], abs=1e-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 c[n] == pytest.approx(d[n], abs=1e-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 c[n] == pytest.approx(d[n], abs=1e-3)
|
