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Barycenter Centrality

Source: R/centrality.R
centrality_barycenter.Rd

Barycenter centrality is the reciprocal of the total shortest-path distance from a node to the nodes it reaches: $$BC(v) = \frac{1}{\sum_{w \ne v} d(v, w)}.$$ Unreachable nodes are left out of the sum.

Usage

centrality_barycenter(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), cutoff (largest path length considered, default -1 for no limit) and normalized (divide by the maximum, default FALSE).

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. The formula is the one centrality_closeness computes, and with the default weighted = TRUE the two agree on every node that reaches another node. A node that reaches no other node scores 0, where closeness returns NaN.

See also

centrality_closeness, centrality_average_distance, centrality.

Examples

centrality_barycenter(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