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# approximate_current_flow_betweenness_centrality¶

approximate_current_flow_betweenness_centrality(G, normalized=True, weight='weight', dtype=<type 'float'>, solver='full', epsilon=0.5, kmax=10000)

Compute the approximate current-flow betweenness centrality for nodes.

Approximates the current-flow betweenness centrality within absolute error of epsilon with high probability [R167].

Parameters : G : graph A NetworkX graph normalized : bool, optional (default=True) If True the betweenness values are normalized by 2/[(n-1)(n-2)] where n is the number of nodes in G. weight : string or None, optional (default=’weight’) Key for edge data used as the edge weight. If None, then use 1 as each edge weight. dtype: data type (float) Default data type for internal matrices. Set to np.float32 for lower memory consumption. solver: string (default=’lu’) Type of linear solver to use for computing the flow matrix. Options are “full” (uses most memory), “lu” (recommended), and “cg” (uses least memory). epsilon: float Absolute error tolerance. kmax: int Maximum number of sample node pairs to use for approximation. nodes : dictionary Dictionary of nodes with betweenness centrality as the value.

Notes

The running time is $$O((1/\epsilon^2)m{\sqrt k} \log n)$$ and the space required is $$O(m)$$ for n nodes and m edges.

If the edges have a ‘weight’ attribute they will be used as weights in this algorithm. Unspecified weights are set to 1.

References

 [R167] (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. 533-544. Springer-Verlag, 2005. http://www.inf.uni-konstanz.de/algo/publications/bf-cmbcf-05.pdf