Optimal shattering of complex networks

TL;DR

This paper investigates optimal strategies for attacking or immunizing complex networks by removing nodes to fragment the network, deriving bounds for various graph models and presenting an efficient attack algorithm.

Contribution

It provides new bounds on the minimal node removal for network fragmentation across different graph models and introduces an optimal polynomial-time attack algorithm.

Findings

Bounds for node removal in random regular graphs

Bounds for Erdős-Rényi and scale-free networks

Degree-based attacks are suboptimal

Abstract

We consider optimal attacks or immunization schemes on different models of random graphs. We derive bounds for the minimum number of nodes needed to be removed from a network such that all remaining components are fragments of negligible size. We obtain bounds for different regimes of random regular graphs, Erd\H{o}s-R\'enyi random graphs, and scale free networks, some of which are tight. We show that the performance of attacks by degree is bounded away from optimality. Finally we present a polynomial time attack algorithm and prove its optimal performance in certain cases.