edge_current_flow_betweenness_centrality(G, normalized=True, weight=None, dtype=<class 'float'>, solver='full')
Current-flow betweenness centrality uses an electrical current model for information spreading in contrast to betweenness centrality which uses shortest paths.
Current-flow betweenness centrality is also known as random-walk betweenness centrality .
Current-flow betweenness can be computed in $O(I(n-1)+mn \log n)$ time , where $I(n-1)$ is the time needed to compute the inverse Laplacian. For a full matrix this is $O(n^3)$ but using sparse methods you can achieve $O(nm{\sqrt k})$ where $k$ is the Laplacian matrix condition number.
The space required is $O(nw)$ where $w$ is the width of the sparse Laplacian matrix. Worse case is $w=n$ for $O(n^2)$.
If the edges have a 'weight' attribute they will be used as weights in this algorithm. Unspecified weights are set to 1.
A NetworkX graph
If True the betweenness values are normalized by 2/[(n-1)(n-2)] where n is the number of nodes in G.
Key for edge data used as the edge weight. If None, then use 1 as each edge weight. The weight reflects the capacity or the strength of the edge.
Default data type for internal matrices. Set to np.float32 for lower memory consumption.
Type of linear solver to use for computing the flow matrix. Options are "full" (uses most memory), "lu" (recommended), and "cg" (uses least memory).
The algorithm does not support DiGraphs. If the input graph is an instance of DiGraph class, NetworkXError is raised.
Dictionary of edge tuples with betweenness centrality as the value.
Compute current-flow betweenness centrality for edges.
The following pages refer to to this document either explicitly or contain code examples using this.
networkx.algorithms.centrality.current_flow_betweenness.current_flow_betweenness_centrality
networkx.algorithms.centrality.current_flow_betweenness_subset.current_flow_betweenness_centrality_subset
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