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 [R158]:

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

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 :	G : graph A bipartite graph nodes : list or iterable (optional) Compute bipartite clustering for these nodes. The default is all nodes in G. mode : string The pariwise bipartite clustering method to be used in the computation. It must be “dot”, “max”, or “min”.
Returns :	clustering : dictionary A dictionary keyed by node with the clustering coefficient value.

See also

robins_alexander_clustering, square_clustering, average_clustering

References

[R158]

(1, 2) 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