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communicability_centrality_exp¶

communicability_centrality_exp(G)

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 nodes:dictionary Dictionary of nodes with communicability centrality as the value. NetworkXError If the graph is not undirected and simple.

See also

communicability
Communicability between all pairs of nodes in G.
communicability_centrality
Communicability centrality for each node of G.

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],

$SC(u)=(e^A)_{uu} .$

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)