Flow Betweenness

Flow betweenness (Freeman, Borgatti and White 1991) sums, over pairs of other nodes \(s\) and \(t\), the flow that passes through the node when a maximum flow is sent from \(s\) to \(t\) with the edge weights as capacities.

Usage

centrality_flow_betweenness(x, ...)

Arguments

x

Network input accepted by centrality.

...

Further arguments to centrality. The measure uses weighted (default TRUE), invert_weights (default NULL, which is TRUE for tna input), alpha (inversion exponent, default 1) and normalized (default FALSE).

Value

A named numeric vector with one score per node, in input node order.

Details

The measure requires the igraph package and raises an error of class cograph_needs_igraph without it. The flow through a node is read from the maximum flow that igraph::max_flow() returns. On a directed network the sum runs over ordered pairs along the edge direction, and on an undirected network over unordered pairs. weighted = FALSE gives every edge capacity one, and invert_weights = TRUE uses \(1/w^\alpha\) as the capacity.

References

Freeman, L. C., Borgatti, S. P., & White, D. R. (1991). Centrality in valued graphs: A measure of betweenness based on network flow. Social Networks, 13(2), 141-154. doi:10.1016/0378-8733(91)90017-N .

See also

centrality_betweenness, centrality_current_flow_betweenness, centrality.

Examples

centrality_flow_betweenness(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>       9.52       6.33      13.60      16.27       6.66       8.19       4.67 
#>   Evaluate     Create      Share 
#>       7.26      12.18      12.88