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.

翻译：现有关于演化网络度相关性的研究通常依赖于微分方程和统计分析，由于固有的随机性，只能获得近似解。为克服这一局限性，我们提出一种改进的马尔可夫链方法，用于建模演化网络中的度相关性。通过重新设计网络演化规则以更准确地反映实际网络动态，我们获得了与真实网络演化高度匹配的拓扑结构。本方法对定向与非定向网络的度相关性演化过程进行建模，并通过仿真验证了理论结果。该工作首次为演化网络模型中的稳态度相关性提供了理论解，适用于更复杂的演化机制及具有方向属性的网络。此外，本方法支持基于任意时刻网络结构的动态特性控制研究，为该领域研究者提供了新的分析工具。