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This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

# Source code for networkx.algorithms.approximation.clustering_coefficient

# -*- coding: utf-8 -*-
#   Fred Morstatter <fred.morstatter@asu.edu>
#   Jordi Torrents <jtorrents@milnou.net>
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>'])

@not_implemented_for('directed')
[docs]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)