Non-Markovian random walks characterize network robustness to nonlocal cascades

TL;DR

This paper introduces a non-Markovian random walk model to better understand how localized perturbations can cause large-scale, nonlocal cascade failures in complex networks, improving upon traditional static or local models.

Contribution

The authors develop a novel dynamical model mapping failure propagation to a self-avoiding, nonlocal random walk, capturing the nonlocal cascade behavior in complex networks.

Findings

Model accurately predicts critical behavior of cascades.

Framework matches well with experiments on real networks.

Quantifies network vulnerability to nonlocal failures.

Abstract

Localized perturbations in a real-world network have the potential to trigger cascade failures at the whole system level, hindering its operations and functions. Standard approaches analytically tackling this problem are mostly based either on static descriptions, such as percolation, or on models where the failure evolves through first-neighbor connections, crucially failing to capture the nonlocal behavior typical of real cascades. We introduce a dynamical model that maps the failure propagation across the network to a self-avoiding random walk that, at each step, has a probability to perform nonlocal jumps toward operational systems' units. Despite the inherent non-Markovian nature of the process, we are able to characterize the critical behavior of the system out of equilibrium, as well as the stopping time distribution of the cascades. Our numerical experiments on synthetic and empirical biological and transportation networks are in excellent agreement with theoretical expectation, demonstrating the ability of our framework to quantify the vulnerability to nonlocal cascade failures of complex systems with interconnected structure.