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node_redundancy¶

node_redundancy
(G, nodes=None)[source]¶ Computes the node redundancy coefficients for the nodes in the bipartite graph
G
.The redundancy coefficient of a node is the fraction of pairs of neighbors of that are both linked to other nodes. In a onemode projection these nodes would be linked together even if were not there.
More formally, for any vertex , the redundancy coefficient of `v` is defined by
where is the set of neighbors of 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 – A dictionary keyed by node with the node redundancy value.
Return type: dictionary
Examples
Compute the redundancy coefficient of each node in a graph:
>>> import networkx as nx >>> 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:
>>> import networkx as nx >>> from networkx.algorithms import bipartite >>> G = nx.cycle_graph(4) >>> rc = bipartite.node_redundancy(G) >>> sum(rc.values()) / len(G) 1.0
Compute the average redundancy for a set of nodes:
>>> import networkx as nx >>> from networkx.algorithms import bipartite >>> G = nx.cycle_graph(4) >>> rc = bipartite.node_redundancy(G) >>> nodes = [0, 2] >>> sum(rc[n] for n in nodes) / len(nodes) 1.0
Raises: NetworkXError
– If any of the nodes in the graph (or innodes
, if specified) has (out)degree less than two (which would result in division by zero, according to the definition of the redundancy coefficient).References
[1] Latapy, Matthieu, Clémence Magnien, and Nathalie Del Vecchio (2008). Basic notions for the analysis of large twomode networks. Social Networks 30(1), 31–48.