Centroid Value

The centroid value (Koschuetzki et al. 2005) compares a node with every other node by the number of nodes each one is closer to. With $\gamma(v, u)$ the number of nodes strictly closer to $v$ than to $u$, $$CV(v) = \min_{u} \left[ \gamma(v, u) - \gamma(u, v) \right].$$ The minimum includes $u = v$, so the score is at most 0, and values closer to 0 mark more central nodes.

Usage

centrality_centroid(x, mode = "all", ...)

Arguments

x: Network input accepted by centrality.
mode: For directed networks: "all" (default), "out" or "in".
...: 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 cutoff (largest path length considered, default -1 for no limit).

Value

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

Details

Edge weights are read as path lengths. invert_weights = TRUE uses $1/w^\alpha$ as the length, and weighted = FALSE counts hops. mode sets the direction of the paths.

References

Koschuetzki, D., Lehmann, K. A., Peeters, L., Richter, S., Tenfelde-Podehl, D., & Zlotowski, O. (2005). Centrality indices. In U. Brandes & T. Erlebach (Eds.), Network Analysis: Methodological Foundations (pp. 16-61). Springer. doi:10.1007/978-3-540-31955-9_3 .

Examples

centrality_centroid(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>         -2         -6         -2         -8         -2         -8         -4 
#>   Evaluate     Create      Share 
#>         -8         -2         -8