average_clustering#

average_clustering(G, trials=1000, seed=None)[source]#

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:

GNetworkX graph
trialsinteger: Number of trials to perform (default 1000).
seedinteger, random_state, or None (default): Indicator of random number generation state. See Randomness.

Returns:

cfloat: Approximated average clustering coefficient.

Raises:

NetworkXNotImplemented: If G is directed.

References

[1]

Schank, Thomas, and Dorothea Wagner. Approximating clustering coefficient and transitivity. Universität Karlsruhe, Fakultät für Informatik, 2004. https://doi.org/10.5445/IR/1000001239

Examples

>>> from networkx.algorithms import approximation
>>> G = nx.erdos_renyi_graph(10, 0.2, seed=10)
>>> approximation.average_clustering(G, trials=1000, seed=10)
0.214