Lin Centrality

Lin centrality divides the squared number of nodes a node reaches by the sum of its distances to them: $$L(i) = \frac{r_i^2}{\sum_{j \in R_i} d_{ij}},$$ where \(R_i\) is the set of \(r_i\) nodes reachable from \(i\). The score is defined on disconnected networks.

Usage

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

Arguments

x

Network input accepted by centrality.

mode

Direction for directed networks: "all" (default), "out" or "in".

...

Further arguments to centrality. The measure uses weighted (default TRUE), invert_weights (default NULL, which inverts for tna input only), alpha (inversion exponent, default 1) and cutoff (largest distance counted, 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 distances. weighted = FALSE uses hop counts, and invert_weights = TRUE converts a weight \(w\) to the distance \(1/w^\alpha\). mode = "all" treats edges as undirected, "out" uses distances from the node and "in" distances to it. A node that reaches no other node scores 0, and a single-node network gives NA. On undirected networks the values equal centiserve::lincent().

See also

centrality_closeness, centrality_harmonic, centrality.

Examples

centrality_lin(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>   41.75258   36.32287   46.28571   30.68182   42.18750   28.02768   39.13043 
#>   Evaluate     Create      Share 
#>   32.66129   42.63158   28.52113