Stochastic Process-based Method for Degree-Degree Correlation of Evolving Networks

TL;DR

This paper introduces a Markov chain-based method to accurately model and analyze the degree correlation in evolving networks, providing the first theoretical steady-state solution applicable to complex and directed networks.

Contribution

It presents an improved Markov chain approach that better reflects real network dynamics, enabling precise theoretical analysis of degree correlation in evolving networks.

Findings

Achieved close match with real-world network evolution structures.

Provided the first theoretical steady-state degree correlation solution.

Validated results through simulations for directed and undirected networks.

Abstract

Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an improved Markov chain method for modeling degree correlation in evolving networks. By redesigning the network evolution rules to reflect actual network dynamics more accurately, we achieve a topological structure that closely matches real-world network evolution. Our method models the degree correlation evolution process for both directed and undirected networks and provides theoretical results that are verified through simulations. This work offers the first theoretical solution for the steady-state degree correlation in evolving network models and is applicable to more complex evolution mechanisms and networks with directional attributes. Additionally, it supports the study of dynamic characteristic control based on network structure at any given time, offering a new tool for researchers in the field.