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Network Robustness Analysis via Node Removal Simulation

robustness_analysis.Rd

Simulates the removal of nodes from a network using various strategies and evaluates how the structure degrades using selected robustness metrics. Useful for assessing the vulnerability or resilience of a graph.

Usage

robustness_analysis(
  graph,
  removal_strategy = c("random", "degree", "betweenness"),
  steps = 50,
  metrics = c("lcc_size", "efficiency", "n_components"),
  n_reps = 50,
  plot = TRUE,
  seed = NULL
)

Arguments

graph

An igraph object representing the network to plot or a data frame containing a symbolic edge list in the first two columns. Additional columns are considered as edge attributes. Must be undirected; directed graphs will be converted.

removal_strategy

Character. Strategy used for node removal. Options are: "random", "degree", "betweenness", or the name of a numeric vertex attribute. Custom attributes are interpreted as priority scores (higher = removed first).

steps

Integer. Number of removal steps (default: 50).

metrics

Character vector. Structural metrics to compute at each step. Options include: "lcc_size", "efficiency", and "n_components".

n_reps

Integer. Number of simulation repetitions (only relevant if removal_strategy = "random").

plot

Logical. If TRUE, a robustness plot is generated.

seed

Integer or NULL. Random seed for reproducibility.

Value

A list with:

all_results

A data frame with simulation results across all steps and repetitions.

summary

A summarized data frame (mean and SD) if n_reps > 1, otherwise raw results.

auc

Named list of AUC (area under the curve) values for each selected metric.

If plot = TRUE, a ggplot object is generated showing the evolution of selected metrics as nodes are progressively removed.

Details

This function builds on classic approaches in network science for evaluating structural robustness (e.g., Albert, Jeong, & Barabási, Nature 2000) by simulating progressive node removal and quantifying the degradation of key topological features.

For deterministic strategies ("degree", "betweenness", or custom attributes), nodes are removed in a fixed priority order. For the "random" strategy, the process is repeated n_reps times, and the results are aggregated.

#' @references Albert R, Jeong H, Barabási AL. Error and attack tolerance of complex networks. Nature. 2000;406(6794):378–382. doi:10.1038/35019019

The function uses:

  • Largest Connected Component (LCC): Size of the largest remaining component.

  • Global Efficiency: Average inverse shortest path length among all pairs.

  • Number of Components: Total number of disconnected components.

Additionally, Area Under the Curve (AUC) is calculated for each metric, providing a scalar summary of robustness. A higher AUC indicates greater resilience (i.e., slower degradation).

The implementation is inspired by principles described in: Albert R, Jeong H, Barabási AL. Error and attack tolerance of complex networks. Nature. 2000;406:378–382. (doi:10.1038/35019019 )

The function uses:

  • Size of the largest connected component (lcc_size)

  • Global efficiency (average inverse shortest path length)

  • Number of components (n_components)

to evaluate how robust the network remains during progressive node failure.

Examples

if (FALSE) { # \dontrun{
g <- igraph::sample_pa(100)
robustness_analysis(g, removal_strategy = "degree", metrics = c("lcc_size", "n_components"))
} # }