def test_converge_to_betweenness(self):
"""percolation centrality: should converge to betweenness
centrality when all nodes are percolated the same"""
# taken from betweenness test test_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,
}
p_states = {k: 1.0 for k, v in b_answer.items()}
p_answer = nx.percolation_centrality(G, states=p_states)
for n in sorted(G):
assert almost_equal(p_answer[n], b_answer[n], places=3)
p_states = {k: 0.3 for k, v in b_answer.items()}
p_answer = nx.percolation_centrality(G, states=p_states)
for n in sorted(G):
assert almost_equal(p_answer[n], b_answer[n], places=3)
def test_converge_to_betweenness(self):
"""percolation centrality: should converge to betweenness
centrality when all nodes are percolated the same"""
# taken from betweenness test test_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}
p_states = {k: 1.0 for k, v in b_answer.items()}
p_answer = nx.percolation_centrality(G, states=p_states)
for n in sorted(G):
assert_almost_equal(p_answer[n], b_answer[n], places=3)
p_states = {k: 0.3 for k, v in b_answer.items()}
p_answer = nx.percolation_centrality(G, states=p_states)
for n in sorted(G):
assert_almost_equal(p_answer[n], b_answer[n], places=3)
def test_converge_to_betweenness(self):
"""percolation centrality: should converge to betweenness
centrality when all nodes are percolated the same"""
# taken from betweenness test test_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}
p_states = {k: 1.0 for k, v in b_answer.items()}
p_answer = nx.percolation_centrality(G, states=p_states)
for n in sorted(G):
assert_almost_equal(p_answer[n], b_answer[n], places=3)
p_states = {k: 0.3 for k, v in b_answer.items()}
p_answer = nx.percolation_centrality(G, states=p_states)
for n in sorted(G):
assert_almost_equal(p_answer[n], b_answer[n], places=3)
def test_percolation_example1b(self):
"""percolation centrality: example 1a"""
G = example1b_G()
p = nx.percolation_centrality(G)
p_answer = {4: 0.825, 6: 0.4}
for n in p_answer:
assert almost_equal(p[n], p_answer[n], places=3)
def test_percolation_example1b(self):
"""percolation centrality: example 1a"""
G = example1b_G()
p = nx.percolation_centrality(G)
p_answer = {4: 0.825, 6: 0.4}
for n in p_answer:
assert p[n] == pytest.approx(p_answer[n], abs=1e-3)
def test_percolation_example1b(self):
"""percolation centrality: example 1a"""
G = example1b_G()
p = nx.percolation_centrality(G)
p_answer = {4: 0.825, 6: 0.4}
for n in p_answer:
assert_almost_equal(p[n], p_answer[n], places=3)
def percolation(G):
balldict = {}
for node in G.nodes:
balldict[node] = G.nodes[node]['superUrn'].Um[0]
centrality = nx.percolation_centrality(G, states=balldict)
return centrality
def Centrality(G,
N=10,
method='katz',
outliers=False,
Label=True,
layOut='shells'):
if method.lower() == 'katz':
phi = 1.618033988749895 # largest eigenvalue of adj matrix
ranking = nx.katz_centrality_numpy(G, 1 / phi)
elif method.lower() == 'degree':
ranking = nx.degree_centrality(G)
elif method.lower() == 'eigen':
ranking = nx.eigenvector_centrality_numpy(G)
elif method.lower() == 'closeness':
ranking = nx.closeness_centrality(G)
elif method.lower() == 'betweeness':
ranking = nx.betweenness_centrality(G)
elif method.lower() == 'harmonic':
ranking = nx.harmonic_centrality(G)
elif method.lower() == 'percolation':
ranking = nx.percolation_centrality(G)
else:
print('Error, Unsupported Method.')
return None
important_nodes = sorted(ranking.items(),
key=operator.itemgetter(1))[::-1] #[0:Nimportant]
data = np.array([n[1] for n in important_nodes])
dnodes = [n[0] for n in important_nodes][:N]
if outliers:
m = 1 # 1 standard Deviation CI
data = data[:N]
out = len(data[abs(data - np.mean(data)) > m *
np.std(data)]) # outlier within m stDev interval
if out < N:
dnodes = [n for n in dnodes[:out]]
print('Influencial Users: {0}'.format(str(dnodes)))
print('Influencial Users Scores: {0}'.format(str(data[:len(dnodes)])))
Gt = G.subgraph(dnodes)
return Gt
def percolation_centrality(G):
return nx.percolation_centrality(G)
def compute_subgraph_center(self, subgraph):
if self.method == 'betweenness_centrality':
d = nx.betweenness_centrality(subgraph, weight='weight')
center = max(d, key=d.get)
elif self.method == 'betweenness_centrality_subset':
d = nx.betweenness_centrality_subset(subgraph, weight='weight')
center = max(d, key=d.get)
elif self.method == 'information_centrality':
d = nx.information_centrality(subgraph, weight='weight')
center = max(d, key=d.get)
elif self.method == 'local_reaching_centrality':
d = {}
for n in self.G.nodes():
d[n] = nx.local_reaching_centrality(self.G, n, weight='weight')
center = max(d, key=d.get)
elif self.method == 'voterank':
d = nx.voterank(subgraph)
center = max(d, key=d.get)
elif self.method == 'percolation_centrality':
d = nx.percolation_centrality(subgraph, weight='weight')
center = max(d, key=d.get)
elif self.method == 'subgraph_centrality':
d = nx.subgraph_centrality(subgraph)
center = max(d, key=d.get)
elif self.method == 'subgraph_centrality_exp':
d = nx.subgraph_centrality_exp(subgraph)
center = max(d, key=d.get)
elif self.method == 'estrada_index':
d = nx.estrada_index(subgraph)
center = max(d, key=d.get)
elif self.method == 'second_order_centrality':
d = nx.second_order_centrality(subgraph)
center = max(d, key=d.get)
elif self.method == 'eigenvector_centrality':
d = nx.eigenvector_centrality(subgraph, weight='weight')
center = max(d, key=d.get)
elif self.method == 'load_centrality':
d = nx.load_centrality(subgraph, weight='weight')
center = max(d, key=d.get)
elif self.method == 'closeness_centrality':
d = nx.closeness_centrality(subgraph)
center = max(d, key=d.get)
elif self.method == 'current_flow_closeness_centrality':
d = nx.current_flow_closeness_centrality(subgraph, weight='weight')
center = max(d, key=d.get)
elif self.method == 'current_flow_betweenness_centrality':
d = nx.current_flow_betweenness_centrality(subgraph,
weight='weight')
center = max(d, key=d.get)
elif self.method == 'current_flow_betweenness_centrality_subset':
d = nx.current_flow_betweenness_centrality_subset(subgraph,
weight='weight')
center = max(d, key=d.get)
elif self.method == 'approximate_current_flow_betweenness_centrality':
d = nx.approximate_current_flow_betweenness_centrality(
subgraph, weight='weight')
center = max(d, key=d.get)
elif self.method == 'harmonic_centrality':
d = nx.harmonic_centrality(subgraph)
center = max(d, key=d.get)
elif self.method == 'page_rank':
d = nx.pagerank(subgraph, weight='weight')
center = max(d, key=d.get)
elif self.method == 'hits':
d = nx.hits(subgraph)
center = max(d, key=d.get)
elif self.method == 'katz_centrality':
d = nx.katz_centrality(subgraph, weight='weight')
center = max(d, key=d.get)
else:
new_centers = nx.center(subgraph)
# new_centers gives a list of centers and here we just pick one randomly --not good for stability
# to do : find a better way to choose the center--make it stable
index = random.randint(0, len(new_centers) - 1)
center = new_centers[index]
return center
def percolation_centrality(G):
G2 = nx.percolation_centrality(G,
attribute='percolation',
states=None,
weight=None)
return G2
