# -*- coding: utf-8 -*-
# Copyright (C) 2013 by
# Fred Morstatter <fred.morstatter@asu.edu>
# Jordi Torrents <jtorrents@milnou.net>
# All rights reserved.
# BSD license.
import random
from networkx.utils import not_implemented_for
__all__ = ['average_clustering']
__author__ = """\n""".join(['Fred Morstatter <fred.morstatter@asu.edu>',
'Jordi Torrents <jtorrents@milnou.net>'])
[docs]@not_implemented_for('directed')
def average_clustering(G, trials=1000):
r"""Estimates the average clustering coefficient of G.
The local clustering of each node in `G` is the fraction of triangles
that actually exist over all possible triangles in its neighborhood.
The average clustering coefficient of a graph `G` is the mean of
local clusterings.
This function finds an approximate average clustering coefficient
for G by repeating `n` times (defined in `trials`) the following
experiment: choose a node at random, choose two of its neighbors
at random, and check if they are connected. The approximate
coefficient is the fraction of triangles found over the number
of trials [1]_.
Parameters
----------
G : NetworkX graph
trials : integer
Number of trials to perform (default 1000).
Returns
-------
c : float
Approximated average clustering coefficient.
References
----------
.. [1] Schank, Thomas, and Dorothea Wagner. Approximating clustering
coefficient and transitivity. Universität Karlsruhe, Fakultät für
Informatik, 2004.
http://www.emis.ams.org/journals/JGAA/accepted/2005/SchankWagner2005.9.2.pdf
"""
n = len(G)
triangles = 0
nodes = G.nodes()
for i in [int(random.random() * n) for i in range(trials)]:
nbrs = list(G[nodes[i]])
if len(nbrs) < 2:
continue
u, v = random.sample(nbrs, 2)
if u in G[v]:
triangles += 1
return triangles / float(trials)