Generalized Closeness

Generalized closeness, as in the tidygraph package, sums a decay factor \(\alpha\) raised to the distance from the node to every node: $$GC(v) = \sum_{w} \alpha^{d(v, w)}.$$ The sum includes the node itself, which adds one to every score, and unreachable nodes contribute 0.

Usage

centrality_generalized_closeness(x, mode = "all", decay_parameter = 0.5, ...)

Arguments

x

Network input accepted by centrality.

mode

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

decay_parameter

Decay factor \(\alpha\) of the formula. Default 0.5.

...

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, with the inversion exponent alpha of centrality, and weighted = FALSE counts hops. mode sets the direction of the paths. The values equal those of centrality_decay with the same decay_parameter, which must lie strictly between 0 and 1; other values raise a cograph_bad_parameter error.

See also

centrality_decay, centrality_harmonic, centrality.

Examples

centrality_generalized_closeness(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>   8.765551   8.592851   8.877387   8.354837   8.781835   8.213449   8.690109 
#>   Evaluate     Create      Share 
#>   8.458391   8.781042   8.238714