Degree Distribution of Evolving Network with Node Preference Deletion

Discussing evolutionary network models and corresponding degree distributions under different mechanisms is applied basic research in network science. This study proposes a new evolutionary network model, which integrates node preference deletion and edge reconnection mechanisms and is also an extension of the existing evolutionary network model. In order to analyze the key statistical property of the model, the steady-state distribution, we propose a Markov chain method based on the enhanced stochastic process rule (ESPR). The ESPR method makes the evolving network’s topological structure and statistical properties consistent with those observed in the natural evolution process, ensures the theoretical results of the degree distribution of the evolving network model, and overcomes the limitations of using empirical methods for approximate analysis. Finally, we verify the accuracy of the steady-state distribution and tail feature estimation of the model through Monte Carlo simulation. This work has laid a solid theoretical foundation for the future development of evolutionary network models and the study of more complex network statistical properties.