efficiencyLM: Latora and Marchiori efficiency
In MiloMonnier/supplynet: Supply network design and robustness assessment tools

Description Usage Arguments Details Value References Examples

Adapted Based on characterisic âth length Intergates spatial distance. Normalized by ideal efficiency, a situation in whihc all nodes are directly connected Unlike average distance, this metric is correctly defined even if the graph is not connected.

1	efficiencyLM(g)

`g`	An igraph object.

For aggregated graphs, road distance cannot be used. Thus, its uses euclidian distance based on x and y vertices attributes.

A numeric between 0 and 1.

Latora, V., & Marchiori, M. (2001). Efficient Behavior of Small-World Networks. Physical Review Letters, 87(19), 198701. https://doi.org/10.1103/PhysRevLett.87.198701

library(igraph)
set.seed(123)
## Generate 100 random spatial networks with increasing density
genGraph = function(p) {
  g = erdos.renyi.game(10, p)
  V(g)$x = runif(10)
  V(g)$y = runif(10)
  g
}
x = seq(0, 1, by=0.01)
lg = lapply(x, genGraph)
## Efficiency increases with density
y = sapply(lg, efficiencyLM)
plot(x, y)
## Local efficiency is average efficiency of local subgraphs
## dg = decompose.graph(g)
## mean(sapply(dg, efficiencyLM))