Markov chain-based method for degree distribution of evolving networks

Abstract In the study of the degree distribution of evolving networks, the theoretical solution of the degree distribution of networks with node preference deletion has not been solved, and accordingly, subsequent application research based on degree distribution cannot be carried out. This paper improves the most efficient method for solving degree distribution, SPR, and proposes an enhanced stochastic process rule-based (ESPR) Markov chain method so that it can handle networks with node preference deletion. By redesigning the evolution rule, ESPR simulates the natural evolution process of networks with node transfer and keeps the topological structure and statistical properties of the network in ESPR consistent with it. Then, based on this rule, the change of network degree distribution can be characterized by the Markov chain, which significantly reduces the complexity of solving the nonlinear problem of node preference deletion. We use two theorems to show that this method not only targets the degree distribution of networks with node preference deletion but is also compatible with the functions of SPR, providing a complete theoretical framework for solving degree distribution. In addition, the method proposed in this paper can be used to study the instantaneous attitude distribution of networks and can be applied to more complex statistical discussions such as degree correlation.