Robustness and modular structure in networks

TL;DR

This paper investigates how overlapping modular structures in networks influence their robustness, revealing that modules can become disconnected before the entire network fails, which challenges traditional percolation-based predictions.

Contribution

It introduces an analytical and empirical study of the impact of overlapping modules on network robustness, highlighting vulnerabilities overlooked by conventional models.

Findings

Modules can become uncoupled before network disintegration

Overlapping modularity increases network vulnerability

Traditional percolation theory underestimates fragility in modular networks

Abstract

Complex networks have recently attracted much interest due to their prevalence in nature and our daily lives [1, 2]. A critical property of a network is its resilience to random breakdown and failure [3-6], typically studied as a percolation problem [7-9] or by modeling cascading failures [10-12]. Many complex systems, from power grids and the Internet to the brain and society [13-15], can be modeled using modular networks comprised of small, densely connected groups of nodes [16, 17]. These modules often overlap, with network elements belonging to multiple modules [18, 19]. Yet existing work on robustness has not considered the role of overlapping, modular structure. Here we study the robustness of these systems to the failure of elements. We show analytically and empirically that it is possible for the modules themselves to become uncoupled or non-overlapping well before the network disintegrates. If overlapping modular organization plays a role in overall functionality, networks may be far more vulnerable than predicted by conventional percolation theory.