Maximally modular structure of growing hyperbolic networks

TL;DR

This paper demonstrates that hyperbolic network models naturally develop highly modular structures as they grow large, even without explicit community mechanisms, supported by analytical and numerical evidence.

Contribution

It reveals that the popularity-similarity optimization model produces highly modular networks in the thermodynamic limit without explicit community formation.

Findings

Modularity approaches one as network size increases

Networks exhibit high clustering and small-world properties

Modular structure emerges naturally in large hyperbolic networks

Abstract

Hyperbolic models are remarkably good at reproducing the scale-free, highly clustered and small-world properties of networks representing real complex systems in a very simple framework. Here we show that for the popularity-similarity optimization model from this family, the generated networks become also extremely modular in the thermodynamic limit, in spite of lacking any explicit community formation mechanism in the model definition. According to our analytical results supported by numerical simulations, when the system size is increased, the modularity approaches one surprisingly fast.