average_clustering

average_clustering(G, nodes=None, mode='dot')

Compute the average bipartite clustering coefficient.

A clustering coefficient for the whole graph is the average,

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

where n is the number of nodes in G.

Similar measures for the two bipartite sets can be defined [1]

\[C_X = \frac{1}{|X|}\sum_{v \in X} c_v,\]

where X is a bipartite set of G.

Parameters

Ggraph

a bipartite graph

nodeslist or iterable, optional

A container of nodes to use in computing the average. The nodes should be either the entire graph (the default) or one of the bipartite sets.

modestring

The pariwise bipartite clustering method. It must be “dot”, “max”, or “min”

Returns

clusteringfloat

The average bipartite clustering for the given set of nodes or the entire graph if no nodes are specified.

See also

clustering

Notes

The container of nodes passed to this function must contain all of the nodes in one of the bipartite sets (“top” or “bottom”) in order to compute the correct average bipartite clustering coefficients. See bipartite documentation for further details on how bipartite graphs are handled in NetworkX.

References

1

Latapy, Matthieu, Clémence Magnien, and Nathalie Del Vecchio (2008). Basic notions for the analysis of large two-mode networks. Social Networks 30(1), 31–48.

Examples

>>> from networkx.algorithms import bipartite
>>> G = nx.star_graph(3)  # star graphs are bipartite
>>> bipartite.average_clustering(G)
0.75
>>> X, Y = bipartite.sets(G)
>>> bipartite.average_clustering(G, X)
0.0
>>> bipartite.average_clustering(G, Y)
1.0