Domain Proximity Prestige

Domain proximity prestige (Wasserman and Faust 1994) combines the number of nodes that reach a node with their distance to it: $$PD(v) = \frac{R_v^2}{(n - 1)\,D_v},$$ where $R_v$ is the number of other nodes with a directed path to $v$ and $D_v$ the sum of their hop distances to $v$.

Usage

centrality_prestige_domain_proximity(x, ...)

Arguments

x: Network input accepted by centrality.
...: Further arguments to centrality.

Value

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

Details

The measure needs a directed network. On undirected input every score is NA with a cograph_undefined_measure warning. Edge weights are ignored. A node that no other node reaches scores 0, and the score lies between 0 and 1. On strongly connected networks the values equal sna::prestige(cmode = "domain.proximity"). On other networks sna sets some scores to 0, because its sum multiplies an infinite distance by zero; cograph sums the finite distances only.

References

Wasserman, S., & Faust, K. (1994). Social Network Analysis: Methods and Applications. Cambridge University Press.

Examples

centrality_prestige_domain_proximity(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>  0.6428571  0.4500000  0.7500000  0.5625000  0.5625000  0.4736842  0.3913043 
#>   Evaluate     Create      Share 
#>  0.4736842  0.5625000  0.5625000