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# 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”. clustering – A dictionary keyed by node with the clustering coefficient value. 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


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.