swan_combinatory function

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.

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.

Returns

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.

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)

References

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