Interdependent transport via percolation backbones in spatial networks

TL;DR

This paper investigates how interdependence affects transport in spatial networks, revealing increased vulnerability and phase transition behaviors when considering the network's backbone rather than just the giant component.

Contribution

It introduces a model of interdependent resistor networks with spatial constraints, analyzing their vulnerability and phase transitions compared to traditional percolation models.

Findings

Interdependent resistor networks are more vulnerable than percolation-based networks.

First-order phase transitions occur at link-lengths where the mutual giant component still forms.

Dandling ends play a crucial role in the increased vulnerability.

Abstract

The functionality of nodes in a network is often described by the structural feature of belonging to the giant component. However, when dealing with problems like transport, a more appropriate functionality criterion is for a node to belong to the network's backbone, where the flow of information and of other physical quantities (such as current) occurs. Here we study percolation in a model of interdependent resistor networks and show the effect of spatiality on their coupled functioning. We do this on a realistic model of spatial networks, featuring a Poisson distribution of link-lengths. We find that interdependent resistor networks are significantly more vulnerable than their percolation-based counterparts, featuring first-order phase transitions at link-lengths where the mutual giant component still emerges continuously. We explain this apparent contradiction by tracing the origin of the increased vulnerability of interdependent transport to the crucial role played by the dandling ends. Moreover, we interpret these differences by considering an heterogeneous $k$-core percolation process which enables to define a one-parameter family of functionality criteria whose constraints become more and more stringent. Our results highlight the importance that different definitions of nodes functionality have on the collective properties of coupled processes, and provide better understanding of the problem of interdependent transport in many real-world networks.