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node_redundancy(G, nodes=None)[source]

Compute bipartite node redundancy coefficient.

The redundancy coefficient of a node \(v\) is the fraction of pairs of neighbors of \(v\) that are both linked to other nodes. In a one-mode projection these nodes would be linked together even if \(v\) were not there.

\[rc(v) = \frac{|\{\{u,w\} \subseteq N(v), \: \exists v' \neq v,\: (v',u) \in E\: \mathrm{and}\: (v',w) \in E\}|}{ \frac{|N(v)|(|N(v)|-1)}{2}}\]

where \(N(v)\) are the neighbors of \(v\) in \(G\).

Parameters :

G : graph

A bipartite graph

nodes : list or iterable (optional)

Compute redundancy for these nodes. The default is all nodes in G.

Returns :

redundancy : dictionary

A dictionary keyed by node with the node redundancy value.


[R164]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.


>>> from networkx.algorithms import bipartite
>>> G = nx.cycle_graph(4)
>>> rc = bipartite.node_redundancy(G)
>>> rc[0]

Compute the average redundancy for the graph:

>>> sum(rc.values())/len(G)

Compute the average redundancy for a set of nodes:

>>> nodes = [0, 2]
>>> sum(rc[n] for n in nodes)/len(nodes)