Impact on farness when a node is removed — swan

swan_efficiency measures the change in the sum of distances between all node pairs when excluding a node from the network.

Usage

swan_efficiency(g)

Arguments

g

An igraph object representing the graph to analyze. swan_efficiency is based on geographic accessibility, similar to indices used for assessing transportation network performance, such as closeness accessibility. It quantifies the impact of node removal by calculating the change in the sum of distances between all node pairs.

The code is an adaptation from the NetSwan package that was archived on CRAN.

Value

A numeric vector where each entry represents the swan_efficiency value for the corresponding node.

References

Lhomme S. (2015). Analyse spatiale de la structure des réseaux techniques dans un contexte de risques. Cybergeo: European Journal of Geography.

Examples

library(igraph)
# Example graph (electrical network structure)
elec <- matrix(ncol = 2, byrow = TRUE, c(
  11,1, 11,10, 1,2, 2,3, 2,9,
  3,4, 3,8, 4,5, 5,6, 5,7,
  6,7, 7,8, 8,9, 9,10
))
gra <- graph_from_edgelist(elec, directed = FALSE)

# Compute efficiency impact of node removal
f2 <- swan_efficiency(gra)
bet <- betweenness(gra)
reg <- lm(bet ~ f2)
summary(reg)
#> 
#> Call:
#> lm(formula = bet ~ f2)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -1.0956 -0.5924  0.1723  0.4648  1.3389 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)  0.98463    0.38203   2.577   0.0298 *  
#> f2           0.39052    0.01891  20.648 6.85e-09 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.8021 on 9 degrees of freedom
#> Multiple R-squared:  0.9793,	Adjusted R-squared:  0.977 
#> F-statistic: 426.3 on 1 and 9 DF,  p-value: 6.854e-09
#>