Note

This documents the development version of NetworkX. Documentation for the current release can be found here.

networkx.algorithms.centrality.approximate_current_flow_betweenness_centrality

approximate_current_flow_betweenness_centrality(G, normalized=True, weight=None, dtype=<class 'float'>, solver='full', epsilon=0.5, kmax=10000, seed=None)[source]

Compute the approximate current-flow betweenness centrality for nodes.

Approximates the current-flow betweenness centrality within absolute error of epsilon with high probability 1.

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=None)) – 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=’full’)) – 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.

  • seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness.

Returns

nodes – Dictionary of nodes with betweenness centrality as the value.

Return type

dictionary

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

1

Ulrik Brandes and Daniel Fleischer: Centrality Measures Based on Current Flow. Proc. 22nd Symp. Theoretical Aspects of Computer Science (STACS ‘05). LNCS 3404, pp. 533-544. Springer-Verlag, 2005. http://algo.uni-konstanz.de/publications/bf-cmbcf-05.pdf