Dynamics-Driven Evolution to Structural Heterogeneity in Complex Networks

TL;DR

This paper investigates how slow, feedback-driven structural evolution in networks, influenced by local opinion dynamics, leads to highly heterogeneous, small-world structures with hubs, resembling biological and social systems.

Contribution

It demonstrates that slow structural evolution under local opinion feedback results in complex, heterogeneous network topologies with power-law degree distributions.

Findings

Networks evolve into small-world with global hubs.

Slower structural change improves dynamical performance.

Heterogeneity arises from dynamics-structure feedback mechanisms.

Abstract

The mutual influence of dynamics and structure is a central issue in complex systems. In this paper we study by simulation slow evolution of network under the feedback of a local-majority-rule opinion process. If performance-enhancing local mutations have higher chances of getting integrated into its structure, the system can evolve into a highly heterogeneous small-world with a global hub (whose connectivity is proportional to the network size), strong local connection correlations and power law-like degree distribution. Networks with better dynamical performance are achieved if structural evolution occurs much slower than the network dynamics. Structural heterogeneity of many biological and social dynamical systems may also be driven by various dynamics-structure coupling mechanisms.