Modularity produces small-world networks with dynamical time-scale separation

TL;DR

This paper demonstrates that modular organization in networks naturally leads to small-world properties with distinct time-scale separation between local and global dynamics, applicable across various processes.

Contribution

It reveals that modularity in random networks inherently produces small-world features with characteristic dynamical time-scale separation, a universal property across different processes.

Findings

Modular networks exhibit small-world properties.

Time-scale separation distinguishes intra- and inter-modular processes.

Universality across processes like synchronization and diffusion.

Abstract

The functional consequences of local and global dynamics can be very different in natural systems. Many such systems have a network description that exhibits strong local clustering as well as high communication efficiency, often termed as small-world networks (SWN). We show that modular organization in otherwise random networks generically give rise to SWN, with a characteristic time-scale separation between fast intra-modular and slow inter-modular processes. The universality of this dynamical signature, that distinguishes modular networks from earlier models of SWN, is demonstrated by processes as different as spin-ordering, synchronization and diffusion.