Proximal Betweenness Centrality

Proximal betweenness (Brandes 2008, section 3.2) is the fraction of shortest paths on which a node is the last intermediate node before the destination (proximal source) or the first intermediate node after the source (proximal target). Each reachable ordered pair of nodes contributes one unit, divided equally among its shortest paths.

Usage

centrality_proximal_betweenness(x, proximal_variant = "source", ...)

Arguments

x

Network input accepted by centrality.

proximal_variant

"source" (default), "target", "sum" or "union".

...

Further arguments to centrality, such as normalized (divide by the maximum, default FALSE).

Value

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

Details

Shortest paths are counted with unit edge lengths on the simple network, so direction is kept and weights, loops and parallel edges are ignored. Ordered pairs are counted on undirected networks as well, so the scores are not halved. Endpoints are excluded, and paths with fewer than two edges contribute nothing. On an undirected network the source and target variants agree, and "sum" is twice either of them. The "union" variant counts a node once when a two-edge path makes it both proximal source and proximal target. Isolated nodes and every node of a complete graph score zero.

References

Brandes, U. (2008). On variants of shortest-path betweenness centrality and their generic computation. Social Networks, 30, 136-145. doi:10.1016/j.socnet.2007.11.001 .

See also

centrality_betweenness, centrality_stress, centrality.

Examples

centrality_proximal_betweenness(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>   4.600000   8.083333   6.733333  14.750000   2.500000   2.933333   4.233333 
#>   Evaluate     Create      Share 
#>   2.266667   6.833333   7.066667