Return communicability centrality for each node in 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 computes eigenvalues and eigenvectors of the adjacency matrix.
Communicability centrality of a node \(u\) in G can be found using a spectral decomposition of the adjacency matrix [R175] [R176],
where \(v_j\) is an eigenvector of the adjacency matrix \(A\) of G corresponding corresponding to the eigenvalue \(\lambda_j\).
References
[R175] | (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 |
[R176] | (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(G)