Formation of Modularity in a Model of Evolving Networks

TL;DR

This paper presents a dynamical model of evolving social networks demonstrating how modular structures and community formations emerge naturally through local interaction rules and varying coupling strengths.

Contribution

It introduces a novel coevolution model linking network dynamics and topology, explaining the spontaneous emergence of modularity and community structures.

Findings

Low coupling leads to homogeneous, unsynchronized networks.

High coupling results in community formation with modular topology.

Degree and community size follow power-law distributions.

Abstract

Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the observations of real social networks, we introduced a link-creating/deleting strategy according to the local dynamics in the model. Thus the coevolution of dynamics and topology naturally determines the network properties. It is found that for a small coupling strength, the networked system cannot reach any synchronization and the network topology is homogeneous. Interestingly, when the coupling strength is large enough, the networked system spontaneously forms communities with different dynamical states. Meanwhile, the network topology becomes heterogeneous with modular structures. It is further shown that in a certain parameter regime, both the degree and the community size in the formed network follow a power-law distribution, and the networks are found to be assortative. These results are consistent with the characteristics of many empirical networks, and are helpful to understand the mechanism of formation of modularity in complex networks.