Avoiding catastrophic failure in correlated networks of networks

TL;DR

This paper investigates how interconnected networks, like brain networks, can remain stable despite the risk of abrupt failures, revealing that hub-based connections with moderate convergence promote robustness.

Contribution

It provides a theoretical framework showing that hub-based interconnections with moderate convergence ensure stability in networks of networks, supported by empirical brain network experiments.

Findings

Networks connected via hubs with moderate convergence are stable.

Brain networks exhibit topologies that maximize stability.

Theoretical predictions are validated in functional brain network experiments.

Abstract

Networks in nature do not act in isolation but instead exchange information, and depend on each other to function properly. An incipient theory of Networks of Networks have shown that connected random networks may very easily result in abrupt failures. This theoretical finding bares an intrinsic paradox: If natural systems organize in interconnected networks, how can they be so stable? Here we provide a solution to this conundrum, showing that the stability of a system of networks relies on the relation between the internal structure of a network and its pattern of connections to other networks. Specifically, we demonstrate that if network inter-connections are provided by hubs of the network and if there is a moderate degree of convergence of inter-network connection the systems of network are stable and robust to failure. We test this theoretical prediction in two independent experiments of functional brain networks (in task- and resting states) which show that brain networks are connected with a topology that maximizes stability according to the theory.