Abstract: This paper proposes logistic saturated growing model and (M, r) saturated growing model, which overcome the uncertainty of initial network about BA model. Besides, two kinds of saturated growing models are more in accordance with real networks about the growth of edges than BA model. Using Markov chain approach to analyze two models, it obtains matrix iterative formula of node degree distributions. Through numerical calculation, results show that their node degree distributions are subject to power law with decay index -3.25 and -3.18 respectively. In addition, it makes computer simulation of algorithms, and simulation results show the correctness of the theoretical analysis and the time dependence of node degree distributions.

Key words: saturated growing models, scale-free networks, Markov chain, degree distribution

摘要： 提出Logistic饱和增长模型和(M, r)饱和增长模型，这2种模型克服了BA模型初始网络的不明确性，更符合现实网络连线数随着时间的增长规律。采用马氏链方法，分析得到2种模型网络结点度分布的矩阵迭代公式。数值计算结果显示，2种饱和模型的网络结点度分别服从衰减指数?=-3.25和?=-3.18的幂律分布。同时，对2种饱和模型进行计算机模拟，并与马氏链矩阵迭代公式的数值计算结果相比，从而验证理论分析的正确性，也阐明2种饱和模型关于时间是不稳定的。

关键词: 饱和增长模型, 无标度网络, 马氏链, 度分布

CLC Number: 

• TP393

• N94