Betweenness Centrality

Betweenness centrality (Freeman 1977) sums, over pairs of other nodes, the fraction of shortest paths between them that pass through the node: $$B(v) = \sum_{s \ne v \ne t} \frac{\sigma_{st}(v)}{\sigma_{st}},$$ where $\sigma_{st}$ is the number of shortest paths from $s$ to $t$ and $\sigma_{st}(v)$ the number of those through $v$.

Usage

centrality_betweenness(x, ...)

Arguments

x: Network input accepted by centrality.
...: Further arguments to centrality. The measure uses invert_weights (default NULL, which is TRUE for tna input), alpha (inversion exponent, default 1), cutoff (largest path length considered, default -1 for no limit) and normalized (default FALSE).

Value

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

Details

On a directed network the sum runs over ordered pairs along the edge direction, and on an undirected network over unordered pairs. Edge weights are read as path lengths, and invert_weights = TRUE uses $1/w^\alpha$ instead. weighted = FALSE uses hop counts. cutoff drops paths longer than the given length. normalized = TRUE divides the scores by their maximum.

References

Freeman, L. C. (1977). A set of measures of centrality based on betweenness. Sociometry, 40(1), 35-41. doi:10.2307/3033543 .

Examples

centrality_betweenness(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>        5.0       15.5       18.0       15.0       10.0        0.5        6.5 
#>   Evaluate     Create      Share 
#>        3.0       13.0        9.0