Spreading of localized attacks on spatial multiplex networks with a community structure

TL;DR

This paper investigates how localized attacks can cause cascading failures in spatial multiplex networks with community structures, revealing a critical damage size that leads to system collapse.

Contribution

It introduces an analytical method to study localized attack effects on community-structured spatial multiplex networks, supported by simulation validation.

Findings

A critical localized damage size causes system-wide collapse.

The analytical model accurately predicts attack spreading.

Connectivity and spatial parameters influence attack vulnerability.

Abstract

We study the effect of localized attacks on a multiplex spatial network, where each layer is a network of communities. The system is considered functional when the nodes belong to the giant component in all the multiplex layers. The communities are of linear size $\zeta$, such that within them any pair of nodes are linked with same probability, and additionally nodes in nearby communities are linked with a different (typically smaller) probability. This model can represent an interdependent infrastructure system of cities where within the city there are many links while between cities there are fewer links. We develop an analytical method, similar to the finite element method applied to a network with communities, and verify our analytical results by simulations. We find, both by simulation and theory, that for different parameters of connectivity and spatiality --- there is a critical localized size of damage above which it will spread and the entire system will collapse.