rich_club_coefficient(G, normalized=True, Q=100)¶
Return the rich-club coefficient of the graph G.
The rich-club coefficient is the ratio, for every degree k, of the number of actual to the number of potential edges for nodes with degree greater than k:
where Nk is the number of nodes with degree larger than k, and Ek be the number of edges among those nodes.
- G (NetworkX graph) –
- normalized (bool (optional)) – Normalize using randomized network (see )
- Q (float (optional, default=100)) – If normalized=True build a random network by performing Q*M double-edge swaps, where M is the number of edges in G, to use as a null-model for normalization.
rc – A dictionary, keyed by degree, with rich club coefficient values.
>>> G = nx.Graph([(0,1),(0,2),(1,2),(1,3),(1,4),(4,5)]) >>> rc = nx.rich_club_coefficient(G,normalized=False) >>> rc 0.4
The rich club definition and algorithm are found in . This algorithm ignores any edge weights and is not defined for directed graphs or graphs with parallel edges or self loops.
Estimates for appropriate values of Q are found in .
 (1, 2) Julian J. McAuley, Luciano da Fontoura Costa, and Tibério S. Caetano, “The rich-club phenomenon across complex network hierarchies”, Applied Physics Letters Vol 91 Issue 8, August 2007. http://arxiv.org/abs/physics/0701290  R. Milo, N. Kashtan, S. Itzkovitz, M. E. J. Newman, U. Alon, “Uniform generation of random graphs with arbitrary degree sequences”, 2006. http://arxiv.org/abs/cond-mat/0312028