networkx.algorithms.bipartite.cluster.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

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