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average_clustering

clustering

clustering(G, nodes=None, mode='dot')[source]

Compute a bipartite clustering coefficient for nodes.

The bipartie clustering coefficient is a measure of local density of connections defined as [R122]

System Message: WARNING/2 (c_u = \frac{\sum_{v \in N(N(v))} c_{uv} }{|N(N(u))|})

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where

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are the second order neighbors of

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in

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excluding

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, and

System Message: WARNING/2 (c_{uv})

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is the pairwise clustering coefficient between nodes

System Message: WARNING/2 (u)

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and

System Message: WARNING/2 (v)

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.

The mode selects the function for

System Message: WARNING/2 (c_{uv})

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‘dot’:

System Message: WARNING/2 (c_{uv}=\frac{|N(u)\cap N(v)|}{|N(u) \cup N(v)|})

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‘min’:

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‘max’:

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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.

References

[R122](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 is bipartite
>>> c=bipartite.clustering(G) 
>>> c[0]
0.5
>>> c=bipartite.clustering(G,mode='min') 
>>> c[0]
1.0