Return the communicability centrality for each node of G
Communicability centrality, also called subgraph centrality, of a node \(n\) is the sum of closed walks of all lengths starting and ending at node \(n\).
Parameters: | G: graph : |
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Returns: | nodes:dictionary :
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Raises: | NetworkXError :
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See also
Notes
This version of the algorithm exponentiates the adjacency matrix. The communicability centrality of a node \(u\) in G can be found using the matrix exponential of the adjacency matrix of G [R177] [R178],
References
[R177] | (1, 2) Ernesto Estrada, Juan A. Rodriguez-Velazquez, “Subgraph centrality in complex networks”, Physical Review E 71, 056103 (2005). http://arxiv.org/abs/cond-mat/0504730 |
[R178] | (1, 2) Ernesto Estrada, Naomichi Hatano, “Communicability in complex networks”, Phys. Rev. E 77, 036111 (2008). http://arxiv.org/abs/0707.0756 |
Examples
>>> G = nx.Graph([(0,1),(1,2),(1,5),(5,4),(2,4),(2,3),(4,3),(3,6)])
>>> sc = nx.communicability_centrality_exp(G)