easygraph.functions.centrality.flowbetweenness module

easygraph.functions.centrality.flowbetweenness.flowbetweenness_centrality(G)

Compute the independent-basic betweenness centrality for nodes in a flow network.

\[c_B(v) =\sum_{s,t \in V}\]

rac{sigma(s, t|v)}{sigma(s, t)}

where V is the set of nodes,

\[\sigma(s, t)\ is\ the\ number\ of\ independent\ (s, t)-paths,\]

\[\sigma(s, t|v)\ is\ the\ maximum\ number\ possible\ of\ those\ paths\ passing\ through\ some\ node\ v\ other\ than\ s, t.\]

\[If\ s\ =\ t,\ \sigma(s, t)\ =\ 1,\ and\ if\ v \in \{s, t\},\ \sigma(s, t|v)\ =\ 0\ [2]_.\]

Parameters:

Ggraph

A easygraph directed graph.

Returns:

nodesdictionary

Dictionary of nodes with independent-basic betweenness centrality as the value.

Notes

A flow network is a directed graph where each edge has a capacity and each edge receives a flow.