Network dismantling

TL;DR

This paper investigates the network dismantling problem, proposing a new algorithm and providing theoretical predictions for minimal dismantling sets in large random graphs, highlighting its collective nature.

Contribution

It introduces a three-stage Min-Sum algorithm for network dismantling, extending analysis to heavy-tailed graphs and establishing the problem's collective complexity.

Findings

Precise predictions for minimal dismantling set size in random graphs.

The proposed Min-Sum algorithm efficiently dismantles networks, including heavy-tailed ones.

Optimal dismantling sets are inherently collective, not just a collection of high-performing nodes.

Abstract

We study the network dismantling problem, which consists in determining a minimal set of vertices whose removal leaves the network broken into connected components of sub-extensive size. For a large class of random graphs, this problem is tightly connected to the decycling problem (the removal of vertices leaving the graph acyclic). Exploiting this connection and recent works on epidemic spreading we present precise predictions for the minimal size of a dismantling set in a large random graph with a prescribed (light-tailed) degree distribution. Building on the statistical mechanics perspective we propose a three-stage Min-Sum algorithm for efficiently dismantling networks, including heavy-tailed ones for which the dismantling and decycling problems are not equivalent. We also provide further insights into the dismantling problem concluding that it is an intrinsically collective problem and that optimal dismantling sets cannot be viewed as a collection of individually well performing nodes.