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]:

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

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 – A dictionary keyed by node with the clustering coefficient value.
Return type:	dictionary

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