Robustness of Network of Networks with Interdependent and Interconnected links

TL;DR

This paper develops an analytical and numerical framework to study the robustness of complex network of networks with both interdependent and interconnected links, revealing phase transition behaviors and factors influencing resilience.

Contribution

It introduces a novel framework for analyzing the robustness of network of networks with mixed interdependent and interconnected links, including exact solutions for specific cases.

Findings

System undergoes second to first order phase transition as coupling increases.

Increasing intra- and inter-connectivity links enhances robustness.

Interdependency links decrease the system's robustness.

Abstract

Robustness of network of networks (NON) has been studied only for dependency coupling (J.X. Gao et. al., Nature Physics, 2012) and only for connectivity coupling (E.A. Leicht and R.M. D Souza, arxiv:0907.0894). The case of network of n networks with both interdependent and interconnected links is more complicated, and also more closely to real-life coupled network systems. Here we develop a framework to study analytically and numerically the robustness of this system. For the case of starlike network of n ER networks, we find that the system undergoes from second order to first order phase transition as coupling strength q increases. We find that increasing intra-connectivity links or inter-connectivity links can increase the robustness of the system, while the interdependency links decrease its robustness. Especially when q=1, we find exact analytical solutions of the giant component and the first order transition point. Understanding the robustness of network of networks with interdependent and interconnected links is helpful to design resilient infrastructures.