Understanding network robustness
How much disruption can a complex network withstand, and how can the few units whose loss fragments it be found?
Local failures can propagate through a network, changing its structure and function. Understanding robustness and resilience means asking how much disruption a system can withstand, how it responds and which interventions can reduce the impact.
Our review in Nature Reviews Physics (2024) brings together theoretical and computational approaches to these questions, including the design of robust networks, early-warning signals and adaptive responses. It also compares dismantling techniques and provides ready-to-use scripts.
Network dismantling probes structural vulnerability by finding a small set of units whose removal fragments a network. Finding a minimum set is computationally challenging (NP-hard), so practical approaches often rely on heuristics.
A machine trained to dismantle relatively small systems identifies higher-order topological patterns and disintegrates large-scale social, infrastructural and technological networks more efficiently than human-based heuristics. It also assesses the probability that the next attacks will disintegrate the system, a quantitative early-warning signal of collapse (Nature Communications, 2021).
Latent Geometry-Driven Network Automata use local rules to approximate effective link distances and outperform existing dismantling algorithms, validated on 1,475 real-world networks across 32 domains (ICLR 2026).