Dynamic scaling and universality in evolution of fluctuating random networks

TL;DR

This paper investigates the dynamic scaling behavior of evolving random networks, demonstrating that their size and connectivity follow power-law growth and saturation, with universal features identified through numerical simulations.

Contribution

It introduces a model of evolving random networks exhibiting dynamic scaling and universality, with analysis of how parameters influence network growth and saturation.

Findings

Network size and connectivity grow as power-laws initially

Saturation values and times depend on parameters via power-laws

Universal scaling exponents are identified

Abstract

We found that models of evolving random networks exhibit dynamic scaling similar to scaling of growing surfaces. It is demonstrated by numerical simulations of two variants of the model in which nodes are added as well as removed [Phys. Rev. Lett. 83, 5587 (1999)]. The averaged size and connectivity of the network increase as power-laws in early times but later saturate. Saturated values and times of saturation change with paramaters controlling the local evolution of the network topology. Both saturated values and times of saturation obey also power-law dependences on controlling parameters. Scaling exponents are calculated and universal features are discussed.