Markov chain-based stability analysis of growing networks

TL;DR

This paper applies Markov chain theory to analyze the stability and steady-state degree distribution of growing networks, providing a rigorous mathematical proof and demonstrating the approach's broad applicability.

Contribution

It introduces a Markov chain-based method for stability analysis of growing networks and rigorously derives the steady-state degree distribution for the DMS model.

Findings

Established a relation between growing networks and Markov processes.

Proved the existence of steady-state degree distribution mathematically.

Derived the exact formula for the degree distribution.

Abstract

From the perspective of probability, the stability of growing network is studied in the present paper. Using the DMS model as an example, we establish a relation between the growing network and Markov process. Based on the concept and technique of first-passage probability in Markov theory, we provide a rigorous proof for existence of the steady-state degree distribution, mathematically re-deriving the exact formula of the distribution. The approach based on Markov chain theory is universal and performs well in a large class of growing networks.