This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.
Return communicability betweenness for all pairs of nodes in G.
Communicability betweenness measure makes use of the number of walks connecting every pair of nodes as the basis of a betweenness centrality measure.
Parameters: G (graph) – Returns: nodes – Dictionary of nodes with communicability betweenness as the value. Return type: dictionary Raises:
NetworkXError– If the graph is not undirected and simple.
Let be a simple undirected graph with nodes and edges, and denote the adjacency matrix of .
Let be the graph resulting from removing all edges connected to node but not the node itself.
The adjacency matrix for is , where has nonzeros only in row and column .
The communicability betweenness of a node is 
where is the number of walks involving node r, is the number of closed walks starting at node and ending at node , and is a normalization factor equal to the number of terms in the sum.
The resulting takes values between zero and one. The lower bound cannot be attained for a connected graph, and the upper bound is attained in the star graph.
 Ernesto Estrada, Desmond J. Higham, Naomichi Hatano, “Communicability Betweenness in Complex Networks” Physica A 388 (2009) 764-774. http://arxiv.org/abs/0905.4102
>>> G = nx.Graph([(0,1),(1,2),(1,5),(5,4),(2,4),(2,3),(4,3),(3,6)]) >>> cbc = nx.communicability_betweenness_centrality(G)