Degree-distribution Stability of Growing Networks

TL;DR

This paper introduces a stochastic process model called growing network Markov chains to analyze the degree distribution stability in evolving networks, providing exact formulas and conditions for steady-state distributions.

Contribution

It develops a unified, rigorous method to determine the existence and formulas of steady degree distributions in growing networks using Markov chain analysis.

Findings

Derived conditions for steady degree distribution existence

Obtained exact formulas for degree distributions

Unified approach applicable to various network models

Abstract

In this paper, we abstract a kind of stochastic processes from evolving processes of growing networks, this process is called growing network Markov chains. Thus the existence and the formulas of degree distribution are transformed to the corresponding problems of growing network Markov chains. First we investigate the growing network Markov chains, and obtain the condition in which the steady degree distribution exists and get its exact formulas. Then we apply it to various growing networks. With this method, we get a rigorous, exact and unified solution of the steady degree distribution for growing networks.