Average Distance

Average distance is the sum of the shortest-path distances from a node to every node, divided by \(n + 1\) as in the centiserve package: $$AD(v) = \frac{1}{n + 1} \sum_{w} d(v, w).$$ Lower values mark more central nodes.

Usage

centrality_average_distance(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) 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, and weighted = FALSE counts hops. mode sets the direction of the paths. A node that cannot reach every other node scores Inf, so on a disconnected network every score is Inf.

See also

centrality_barycenter, centrality_closeness, centrality.

Examples

centrality_average_distance(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>  0.1763636  0.2027273  0.1590909  0.2400000  0.1745455  0.2627273  0.1881818 
#>   Evaluate     Create      Share 
#>  0.2254545  0.1727273  0.2581818