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# Source code for networkx.algorithms.bipartite.redundancy

#-*- coding: utf-8 -*-
"""Node redundancy for bipartite graphs."""
[docs]def node_redundancy(G, nodes=None): r"""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. .. math:: 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. 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 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. """ if nodes is None: nodes = G rc = {} for v in nodes: overlap = 0.0 for u, w in combinations(G[v], 2): if len((set(G[u]) & set(G[w])) - set([v])) > 0: overlap += 1 if overlap > 0: n = len(G[v]) norm = 2.0/(n*(n-1)) else: norm = 1.0 rc[v] = overlap*norm return rc