Compute currentflow betweenness centrality for nodes.
Currentflow betweenness centrality uses an electrical current model for information spreading in contrast to betweenness centrality which uses shortest paths.
Currentflow betweenness centrality is also known as randomwalk betweenness centrality [R142].
Parameters :  G : graph
normalized : bool, optional (default=True)
weight : string or None, optional (default=’weight’)
dtype: data type (float) :
solver: string (default=’lu’) :


Returns :  nodes : dictionary

See also
approximate_current_flow_betweenness_centrality, betweenness_centrality, edge_betweenness_centrality, edge_current_flow_betweenness_centrality
Notes
Currentflow betweenness can be computed in time [R141], where is the time needed to compute the inverse Laplacian. For a full matrix this is but using sparse methods you can achieve where is the Laplacian matrix condition number.
The space required is is the width of the sparse Laplacian matrix. Worse case is for .
If the edges have a ‘weight’ attribute they will be used as weights in this algorithm. Unspecified weights are set to 1.
References
[R141]  (1, 2) Centrality Measures Based on Current Flow. Ulrik Brandes and Daniel Fleischer, Proc. 22nd Symp. Theoretical Aspects of Computer Science (STACS ‘05). LNCS 3404, pp. 533544. SpringerVerlag, 2005. http://www.inf.unikonstanz.de/algo/publications/bfcmbcf05.pdf 
[R142]  (1, 2) A measure of betweenness centrality based on random walks, M. E. J. Newman, Social Networks 27, 3954 (2005). 