Error and attack tolerance of complex networks

swan_combinatory assesses network vulnerability and the resistance of networks to node removals, whether due to random failures or intentional attacks.

Usage

swan_combinatory(g, k)

Arguments

g

An igraph object representing the graph to analyze.

k

The number of iterations for assessing the impact of random failures.

Value

A matrix with five columns:

• Column 1: Fraction of nodes removed.

• Column 2: Connectivity loss from betweenness-based attack.

• Column 3: Connectivity loss from degree-based attack.

• Column 4: Connectivity loss from cascading failure.

• Column 5: Connectivity loss from random failures (averaged over k iterations).

Details

Many complex systems display a surprising degree of tolerance against random failures. However, this resilience often comes at the cost of extreme vulnerability to targeted attacks, where removing key nodes (high-degree or high-betweenness nodes) can severely impact network connectivity.

swan_combinatory simulates different attack strategies:

• Random failure: Nodes are removed randomly over multiple iterations.

• Degree-based attack: Nodes are removed in decreasing order of their degree.

• Betweenness-based attack: Nodes are removed in decreasing order of their betweenness centrality.

• Cascading failure: Nodes are removed based on recalculated betweenness after each removal.

The function returns a matrix showing the connectivity loss for each attack scenario.

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

References

Albert R., Jeong H., Barabási A. (2000). Error and attack tolerance of complex networks. Nature, 406(6794), 378-382.

Examples

library(igraph)
# Example electrical network graph
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 vulnerability measures
f4 <- swan_combinatory(gra, 10)