Eccentricity

The eccentricity of a node (Hage and Harary 1995) is its largest shortest-path distance to a node it reaches: $$e(v) = \max_{w:\, d(v, w) < \infty} d(v, w).$$ Lower values mark more central nodes.

Usage

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

centrality_ineccentricity(x, ...)

centrality_outeccentricity(x, ...)

Arguments

x: Network input accepted by centrality.
mode: For directed networks: "all" (default), "out" or "in".
...: Further arguments to centrality, such as directed and normalized.

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 has no effect. weighted = FALSE, or an unweighted input, gives hop counts. mode = "out" follows paths leaving the node and mode = "in" paths arriving at it. centrality_outeccentricity() and centrality_ineccentricity() are these two forms. A node that reaches no other node scores 0.

References

Hage, P., & Harary, F. (1995). Eccentricity and centrality in networks. Social Networks, 17(1), 57-63. doi:10.1016/0378-8733(94)00248-9 .

Examples

centrality_eccentricity(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>       0.33       0.35       0.34       0.39       0.33       0.40       0.38 
#>   Evaluate     Create      Share 
#>       0.40       0.33       0.39