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 [R161] [R162],
SC(u)=\sum_{j=1}^{N}(v_{j}^{u})^2 e^{\lambda_{j}},
where v_j is an eigenvector of the adjacency matrix A of G corresponding corresponding to the eigenvalue \lambda_j.
References
[R161] | (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 |
[R162] | (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)