Local Efficiency — network_local_efficiency • cograph

Computes the average local efficiency across all nodes with igraph::average_local_efficiency(). For each node, igraph removes the node and measures the distances between its neighbors through the rest of the network. The value can therefore exceed the Latora and Marchiori (2001) form, which restricts those distances to the subgraph induced on the neighbors. centrality(x, measures = "local_efficiency") reports the induced-subgraph form. The two agree when the neighbors have no path outside their induced subgraph.

Usage

network_local_efficiency(
  x,
  weights = NULL,
  invert_weights = NULL,
  alpha = 1,
  ...
)

Arguments

x: Network input: matrix, igraph, network, cograph_network, or tna object
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, whose only other argument is directed; anything else raises an "unused argument" error.

Value

Numeric scalar: the average local efficiency, or NA for a graph with fewer than two nodes. For unweighted simple graphs it lies in \([0, 1]\). Weighted graphs can exceed 1 when edge distances are below 1.

Examples

network_local_efficiency(regulation_net)
#> [1] 2.918765