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Return communicability centrality for each node in G.
Communicability centrality, also called subgraph centrality, of a node is the sum of closed walks of all lengths starting and ending at node .
Parameters: G (graph) – Returns: nodes – Dictionary of nodes with communicability centrality as the value. Return type: dictionary Raises:
NetworkXError– If the graph is not undirected and simple.
This version of the algorithm computes eigenvalues and eigenvectors of the adjacency matrix.
where is an eigenvector of the adjacency matrix of G corresponding corresponding to the eigenvalue .
>>> G = nx.Graph([(0,1),(1,2),(1,5),(5,4),(2,4),(2,3),(4,3),(3,6)]) >>> sc = nx.communicability_centrality(G)
 Ernesto Estrada, Juan A. Rodriguez-Velazquez, “Subgraph centrality in complex networks”, Physical Review E 71, 056103 (2005). http://arxiv.org/abs/cond-mat/0504730  Ernesto Estrada, Naomichi Hatano, “Communicability in complex networks”, Phys. Rev. E 77, 036111 (2008). http://arxiv.org/abs/0707.0756