Global Efficiency

Computes the global efficiency of a network, the average of the inverse shortest path lengths between all ordered pairs of distinct nodes. Higher values indicate more efficient global communication. Unreachable pairs contribute 0. A graph with fewer than two nodes returns NA.

Usage

network_global_efficiency(
  x,
  directed = NULL,
  weights = NULL,
  invert_weights = NULL,
  alpha = 1,
  ...
)

Arguments

x

Network input: matrix, igraph, network, cograph_network, or tna object

directed

Logical or NULL. Consider edge direction? Default NULL, which follows the directedness of the converted graph.

weights

Numeric vector of edge weights. Default NULL uses the graph's weight attribute when present. NA ignores weights, so every edge has length 1, whatever invert_weights is.

invert_weights

Logical or NULL. If TRUE, weights are converted to distances as \(1/w^{\alpha}\), so stronger ties give shorter paths. If FALSE, weights are used as distances. Default NULL uses TRUE for tna objects and FALSE otherwise.

alpha

Numeric. Exponent for weight inversion. Default 1.

...

Passed to to_igraph, which accepts no arguments besides directed.

Value

Numeric scalar: the global efficiency. For unweighted simple graphs it lies in \([0, 1]\). Weighted graphs can exceed 1 when edge distances are below 1.

Examples

network_global_efficiency(regulation_net)
#> [1] 3.304491