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
nodes : list or iterable (optional)
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Returns : | redundancy : dictionary
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References
[R83] | 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.cycle_graph(4)
>>> rc = bipartite.node_redundancy(G)
>>> rc[0]
1.0
Compute the average redundancy for the graph:
>>> sum(rc.values())/len(G)
1.0
Compute the average redundancy for a set of nodes:
>>> nodes = [0, 2]
>>> sum(rc[n] for n in nodes)/len(nodes)
1.0