swan_efficiency measures the change in the sum of distances between all node pairs
when excluding a node from the network.
Value
A numeric vector where each entry represents the swan_efficiency value for the
corresponding node.
Details
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.
As in NetSwan, the sum of distances is infinite if the graph is disconnected.
The value of a node is therefore Inf if its removal disconnects the graph and
NaN for all nodes if the graph is already disconnected.
The code is an adaptation from the NetSwan package that was archived on CRAN.
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
#>