average_clustering

average_clustering(G, nodes=None, weight=None, count_zeros=True)

Compute the average clustering coefficient for the graph G.

The clustering coefficient for the graph is the average,

\[C = \frac{1}{n}\sum_{v \in G} c_v,\]

where \(n\) is the number of nodes in G.

Parameters:

Ggraph

nodescontainer of nodes, optional (default=all nodes in G)

Compute average clustering for nodes in this container.

weightstring or None, optional (default=None)

The edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1.

count_zerosbool

If False include only the nodes with nonzero clustering in the average.

Returns:

avgfloat

Average clustering

Notes

This is a space saving routine; it might be faster to use the clustering function to get a list and then take the average.

Self loops are ignored.

References

[1]

Generalizations of the clustering coefficient to weighted complex networks by J. Saramäki, M. Kivelä, J.-P. Onnela, K. Kaski, and J. Kertész, Physical Review E, 75 027105 (2007). http://jponnela.com/web_documents/a9.pdf

[2]

Marcus Kaiser, Mean clustering coefficients: the role of isolated nodes and leafs on clustering measures for small-world networks. https://arxiv.org/abs/0802.2512

Examples

>>> G = nx.complete_graph(5)
>>> print(nx.average_clustering(G))
1.0