Emergence of Robustness in Network of Networks

TL;DR

This paper develops an exact analytical model for percolation transitions in interdependent networks of networks, revealing conditions for robustness and vulnerability in such complex systems.

Contribution

It introduces a new analytical approach to study percolation in Erdős-Rényi NoN, demonstrating robustness and identifying vulnerability patterns.

Findings

Analytical results match numerical simulations

NoN shows robustness against random failures

Identifies interconnectivity patterns leading to vulnerability

Abstract

A model of interdependent networks of networks (NoN) has been introduced recently in the context of brain activation to identify the neural collective influencers in the brain NoN. Here we develop a new approach to derive an exact expression for the random percolation transition in Erd\"{o}s-R\'enyi NoN. Analytical calculations are in excellent agreement with numerical simulations and highlight the robustness of the NoN against random node failures. Interestingly, the phase diagram of the model unveils particular patterns of interconnectivity for which the NoN is most vulnerable. Our results help to understand the emergence of robustness in such interdependent architectures.