Degree-distribution Stability of Evolving Networks

TL;DR

This paper introduces a new method to analyze the degree distribution stability in evolving networks, providing exact formulas and criteria for when the degree distribution follows a power-law.

Contribution

It develops a novel approach transforming the degree distribution problem into evolving network Markov chains, yielding exact and unified solutions.

Findings

Derived exact formulas for degree distribution

Established criteria for power-law stability

Provided a unified solution for steady degree distribution

Abstract

In this paper, we study a class of stochastic processes, called evolving network Markov chains, in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a corresponding problem of evolving network Markov chains. We investigate the evolving network Markov chains, thereby obtaining some exact formulas as well as a precise criterion for determining whether the steady degree distribution of the evolving network is a power-law or not. With this new method, we finally obtain a rigorous, exact and unified solution of the steady degree distribution of the evolving network.