Modularity from fluctuations in random graphs and complex networks

TLDR

The mechanisms by which modularity emerges in complex networks are not well understood, though recent reports suggest it may arise from evolutionary selection. The study demonstrates that stochastic network models generate modular networks due to fluctuations. The authors show that modularity in networks is analogous to the ground‑state energy of a spin system, that random graphs and scale‑free networks exhibit modularity both numerically and analytically, and that this must be considered when defining statistically significant modularity.

Abstract

The mechanisms by which modularity emerges in complex networks are not well understood but recent reports have suggested that modularity may arise from evolutionary selection. We show that finding the modularity of a network is analogous to finding the ground-state energy of a spin system. Moreover, we demonstrate that, due to fluctuations, stochastic network models give rise to modular networks. Specifically, we show both numerically and analytically that random graphs and scale-free networks have modularity. We argue that this fact must be taken into consideration to define statistically significant modularity in complex networks.