rich_club_coefficient(G, normalized=True, Q=100, seed=None)
For each degree k, the rich-club coefficient is the ratio of the number of actual to the number of potential edges for nodes with degree greater than k:
$$\phi(k) = \frac{2 E_k}{N_k (N_k - 1)}$$where :None:None:`N_k` is the number of nodes with degree larger than k, and :None:None:`E_k` is the number of edges among those nodes.
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 .
Undirected graph with neither parallel edges nor self-loops.
Normalize using randomized network as in
If :None:None:`normalized` is True, perform :None:None:`Q * m` double-edge swaps, where m is the number of edges in G, to use as a null-model for normalization.
Indicator of random number generation state. See Randomness<randomness>
.
A dictionary, keyed by degree, with rich-club coefficient values.
Returns the rich-club coefficient of the graph G.
>>> G = nx.Graph([(0, 1), (0, 2), (1, 2), (1, 3), (1, 4), (4, 5)])See :
... rc = nx.rich_club_coefficient(G, normalized=False, seed=42)
... rc[0] 0.4
The following pages refer to to this document either explicitly or contain code examples using this.
networkx.algorithms.richclub.rich_club_coefficient
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