Geodesic K-Reach Centrality

Geodesic k-reach centrality (Borgatti and Everett 2006) counts the nodes that lie within shortest-path distance \(k\) of a node.

Usage

centrality_kreach(x, mode = "all", k = 3, ...)

Arguments

x: Network input accepted by centrality.
mode: Direction for directed networks: "all" (default), "out" or "in".
k: Largest distance counted, a positive number (default 3).
...: Further arguments to centrality. The measure uses invert_weights (default NULL, which inverts for tna input only) and alpha (inversion exponent, default 1).

Value

A named integer vector with one count per node, in input node order.

Details

Edge weights are read as distances, so on a weighted network \(k\) is compared with the summed weights along a path; on regulation_net, whose weights lie below one, every node reaches all others within \(k = 1\). invert_weights = TRUE converts a weight \(w\) to the distance \(1/w^\alpha\). weighted = FALSE uses hop counts. mode = "all" treats edges as undirected, "out" counts nodes reached from the node and "in" nodes that reach it. A k of zero or below raises a cograph_bad_parameter error.

References

Borgatti, S. P., & Everett, M. G. (2006). A graph-theoretic perspective on centrality. Social Networks, 28(4), 466-484. doi:10.1016/j.socnet.2005.11.005 .

Examples

centrality_kreach(regulation_net, k = 0.2)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>          4          3          6          2          4          1          3 
#>   Evaluate     Create      Share 
#>          2          5          0