import networkx as nx
import numpy as np
def random_reference(G, niter=1, connectivity=True, seed=None):
if G.is_directed():
msg = "random_reference() not defined for directed graphs."
raise nx.NetworkXError(msg)
if len(G) < 4:
raise nx.NetworkXError("Graph has less than four nodes.")
from networkx.utils import cumulative_distribution, discrete_sequence
local_conn = nx.connectivity.local_edge_connectivity
G = G.copy()
keys, degrees = zip(*G.degree()) # keys, degree
cdf = cumulative_distribution(degrees) # cdf of degree
nnodes = len(G)
nedges = nx.number_of_edges(G)
niter = niter * nedges
ntries = int(nnodes * nedges / (nnodes * (nnodes - 1) / 2))
swapcount = 0
for i in range(niter):
n = 0
while n < ntries:
# pick two random edges without creating edge list
# choose source node indices from discrete distribution
(ai, ci) = discrete_sequence(2, cdistribution=cdf, seed=seed)
if ai == ci:
continue # same source, skip
a = keys[ai] # convert index to label
c = keys[ci]
# choose target uniformly from neighbors
b = seed.choice(list(G.neighbors(a)))
d = seed.choice(list(G.neighbors(c)))
bi = keys.index(b)
di = keys.index(d)
if b in [a, c, d] or d in [a, b, c]:
continue # all vertices should be different
# don't create parallel edges
if (d not in G[a]) and (b not in G[c]):
G.add_edge(a, d)
G.add_edge(c, b)
G.remove_edge(a, b)
G.remove_edge(c, d)
# Check if the graph is still connected
if connectivity and local_conn(G, a, b) == 0:
# Not connected, revert the swap
G.remove_edge(a, d)
G.remove_edge(c, b)
G.add_edge(a, b)
G.add_edge(c, d)
else:
swapcount += 1
break
n += 1
return G
def sigma(G, niter=100, nrand=10, seed=None):
randMetrics = {"C": [], "L": []}
for i in range(nrand):
Gr = random_reference(G, niter=niter, seed=seed)
randMetrics["C"].append(nx.transitivity(Gr))
randMetrics["L"].append(nx.average_shortest_path_length(Gr))
C = nx.transitivity(G)
L = nx.average_shortest_path_length(G)
Cr = np.mean(randMetrics["C"])
Lr = np.mean(randMetrics["L"])
sigma = (C / Cr) / (L / Lr)
return sigma
if __name__ == "__main__":
print(sigma(G))
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