  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.
