Master-equation analysis of accelerating networks

TL;DR

This paper introduces a master-equation approach to analyze the degree distributions of accelerating networks with time-dependent growth rates, providing exact solutions and connecting non-equilibrium networks to classical random graphs.

Contribution

It applies a master-equation method to derive full time-dependent degree distributions for accelerating networks, a novel approach compared to previous mean-field techniques.

Findings

Exact time-dependent degree distributions derived for accelerating networks.

Good agreement between analytical results and simulations.

Accelerating networks with random attachment are equivalent to classical random graphs.

Abstract

In many real-world networks, the rates of node and link addition are time dependent. This observation motivates the definition of accelerating networks. There has been relatively little investigation of accelerating networks and previous efforts at analyzing their degree distributions have employed mean-field techniques. By contrast, we show that it is possible to apply a master-equation approach to such network development. We provide full time-dependent expressions for the evolution of the degree distributions for the canonical situations of random and preferential attachment in networks undergoing constant acceleration. These results are in excellent agreement with results obtained from simulations. We note that a growing, non-equilibrium network undergoing constant acceleration with random attachment is equivalent to a classical random graph, bridging the gap between non-equilibrium and classical equilibrium networks.