Modularity from Fluctuations in Random Graphs and Complex Networks

TL;DR

This paper demonstrates that modularity in complex networks can naturally emerge from fluctuations in random graph models, highlighting the importance of considering stochastic effects when analyzing network modularity.

Contribution

It establishes a connection between network modularity and spin system ground states, showing that randomness can induce modularity in various network models.

Findings

Random graphs and scale-free networks exhibit inherent modularity due to fluctuations.

Modularity can be analytically and numerically demonstrated in stochastic network models.

The results suggest the need for statistical significance criteria in modularity analysis.

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.