For simple graphs. Mathematical definitions are here.
import numpy as np
import networkx as nx
import community
def Assortativity(ug):
# eij: fraction of edges in a network that connect a node with degree i to one of degree j.
d = max(dict(ug.degree()).values())
e = np.zeros([d,d])
n_edges = len(ug.edges())
for i,j in ug.edges():
d1 = ug.degree(i) # degree of node i
d2 = ug.degree(j) # degree of node j
e[d1-1,d2-1] += 1
e[d2-1,d1-1] += 1
e /= e.sum()
a = e.sum(axis=0)
b = e.sum(axis=1)
ab = np.dot(a,b)
r = (np.diag(e).sum() - ab) / (1. - ab)
return r
def Modularity(ug):
# required packages: community, python-louvain
# commnity detection with louvain algorithm
part = community.best_partition(subg)
Q = community.modularity(part,subg)
return Q
def NormalizedDegreeVariance(ug):
# Keith Smith
n = len(ug.nodes())
m = len(ug.edges())
d = 2.*m / (n*(n-1)) # density: the nubmer of edges divided by tot. possible number of edges
v = np.var(list(dict(ug.degree).values())) # variance in degrees
return v*(n-1.) / (n*m*(1.-d))
def AverageClusteringCoefficient(ug):
return nx.average_clustering(ug)
def Efficiency(ug):
n = len(ug)
denom = n * (n - 1.)
if denom != 0:
g_eff = 0
for i in nx.all_pairs_shortest_path_length(ug):
x = i[1].values()
for j in x:
if j != 0:
g_eff += 1./float(j)
return g_eff / denom
else:
return 0.
