The "weak" interdependence of infrastructure systems produces mixed percolation transitions in multilayer networks

TL;DR

This paper introduces a multilayer network model with weak interdependence and a node-to-link failure mechanism, revealing that different layers experience mixed percolation transitions, which impacts infrastructure robustness analysis.

Contribution

It presents a novel multilayer network model with weak interdependence and cascade tolerance, showing diverse percolation behaviors across layers, unlike previous models.

Findings

High super degree layers percolate abruptly.

Low super degree layers show mixed transition types.

Weak interdependence causes diverse robustness phenomena.

Abstract

In this work, we propose an interdependent, multilayer network model and percolation process that matches infrastructures better than previous models by allowing some nodes to survive when their interdependent neighbors fail. We consider a node-to-link failure propagation mechanism and establish "weak" interdependence across layers via a tolerance parameter $\alpha$ which quantifies the likelihood that a node survives when one of its interdependent neighbors fails. We measure the robustness of any individual layer by the final size of its giant component. Analytical and numerical results show that weak interdependence produces a striking phenomenon: layers at different positions within the multilayer system experience distinct percolation transitions. Especially, layers with high super degree values percolate in an abrupt manner, while those with low super degree values exhibit both continuous and abrupt transitions. This novel phenomenon we call \emph{mixed percolation transitions} has significant implications for network robustness. Previous results that do not consider cascade tolerance and layer super degree may be under- or over-estimating the vulnerability of real systems. Moreover, since $\alpha$ represents a generic measure of various risk management strategies used to buffer infrastructure assets from cascades, our model reveals how nodal protection activities influence failure dynamics in interdependent, multilayer systems.