clustering

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

Compute a bipartite clustering coefficient for nodes.

The bipartie clustering coefficient is a measure of local density of connections defined as [1]:

\[c_u = \frac{\sum_{v \in N(N(u))} c_{uv} }{|N(N(u))|}\]

where N(N(u)) are the second order neighbors of u in G excluding u, and c_{uv} is the pairwise clustering coefficient between nodes u and v.

The mode selects the function for c_{uv} which can be:

dot:

\[c_{uv}=\frac{|N(u)\cap N(v)|}{|N(u) \cup N(v)|}\]

min:

\[c_{uv}=\frac{|N(u)\cap N(v)|}{min(|N(u)|,|N(v)|)}\]

max:

\[c_{uv}=\frac{|N(u)\cap N(v)|}{max(|N(u)|,|N(v)|)}\]

Parameters:

Ggraph

A bipartite graph

nodeslist or iterable (optional)

Compute bipartite clustering for these nodes. The default is all nodes in G.

modestring

The pariwise bipartite clustering method to be used in the computation. It must be “dot”, “max”, or “min”.

Returns:

clusteringdictionary

A dictionary keyed by node with the clustering coefficient value.

See also

robins_alexander_clustering

average_clustering

networkx.algorithms.cluster.square_clustering

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.path_graph(4)  # path graphs are bipartite
>>> c = bipartite.clustering(G)
>>> c[0]
0.5
>>> c = bipartite.clustering(G, mode="min")
>>> c[0]
1.0