Generalized Network Dismantling

TL;DR

This paper introduces a generalized network dismantling problem that considers non-uniform costs for node removal, providing a scalable spectral method to identify critical nodes for network disruption or protection.

Contribution

It formulates a new generalized problem incorporating node-specific costs and proposes a spectral method based on a novel Laplacian operator to solve large-scale instances.

Findings

Outperforms existing methods in large networks

Handles non-uniform node costs effectively

Provides insights into network vulnerability and robustness

Abstract

Finding the set of nodes, which removed or (de)activated can stop the spread of (dis)information, contain an epidemic or disrupt the functioning of a corrupt/criminal organization is still one of the key challenges in network science. In this paper, we introduce the generalized network dismantling problem, which aims to find the set of nodes that, when removed from a network, results in a network fragmentation into subcritical network components at minimum cost. For unit costs, our formulation becomes equivalent to the standard network dismantling problem. Our non-unit cost generalization allows for the inclusion of topological cost functions related to node centrality and non-topological features such as the price, protection level or even social value of a node. In order to solve this optimization problem, we propose a method, which is based on the spectral properties of a novel node-weighted Laplacian operator. The proposed method is applicable to large-scale networks with millions of nodes. It outperforms current state-of-the-art methods and opens new directions in understanding the vulnerability and robustness of complex systems.