Load Centrality

Load centrality (Goh et al. 2001) sends one unit of load from every node to every other node along shortest paths. At each branching the load is split equally among the shortest-path predecessors, and the score of a node is the total load that passes through it.

Usage

centrality_load(x, ...)

Arguments

x: Network input accepted by centrality.
...: Further arguments to centrality. The measure uses weighted (default TRUE), invert_weights (default NULL, which inverts for tna input only) and alpha (inversion exponent, default 1).

Value

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

Details

Edge weights are read as distances. weighted = FALSE uses hop counts, and invert_weights = TRUE converts a weight \(w\) to the distance \(1/w^\alpha\). Paths follow edge direction on a directed network. The values equal sna::loadcent(), which credits the endpoints of each path as well as the intermediate nodes, so the scores are larger than betweenness.

References

Goh, K.-I., Kahng, B., & Kim, D. (2001). Universal behavior of load distribution in scale-free networks. Physical Review Letters, 87(27), 278701. doi:10.1103/PhysRevLett.87.278701 .

Examples

centrality_load(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>       24.0       34.5       37.0       34.0       29.0       19.5       25.5 
#>   Evaluate     Create      Share 
#>       22.0       32.0       28.0