Closeness Centrality

Closeness centrality (Sabidussi 1966) is the reciprocal of the total shortest-path distance from a node to the nodes it reaches: $$C(v) = \frac{1}{\sum_{w \ne v} d(v, w)}.$$ Unreachable nodes are left out of the sum, as in igraph::closeness().

Usage

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

centrality_incloseness(x, ...)

centrality_outcloseness(x, ...)

Arguments

x: Network input accepted by centrality.
mode: For directed networks: "all" (default), "out" or "in".
...: Further arguments to centrality. The measure uses invert_weights (default NULL, which is TRUE for tna input), alpha (inversion exponent, default 1), cutoff (largest path length considered, default -1 for no limit) and normalized (default FALSE).

Value

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

Details

Edge weights are read as path lengths, and invert_weights = TRUE uses $1/w^\alpha$ instead. weighted = FALSE uses hop counts. mode = "out" follows paths leaving the node and mode = "in" paths arriving at it. centrality_outcloseness() and centrality_incloseness() are these two forms. A node that reaches no other node returns NaN. normalized = TRUE multiplies each score by the number of other nodes the node reaches, as igraph does.

References

Sabidussi, G. (1966). The centrality index of a graph. Psychometrika, 31(4), 581-603. doi:10.1007/BF02289527 .

Examples

centrality_closeness(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>  0.5154639  0.4484305  0.5714286  0.3787879  0.5208333  0.3460208  0.4830918 
#>   Evaluate     Create      Share 
#>  0.4032258  0.5263158  0.3521127