不确定网络及其度分布的马氏链数值分析

Uncertainty Networks and Analysis of Degree Distribution via Markov Chain-based Numerical Method

采用不确定理论的方法,基于BA模型及演化网络模型,通过在择优概率的基础上加入不确定变量,提出一个能较好描述现实复杂网络特征的不确定演化网络模型。针对该模型,运用马氏链数值方法,根据连线增加和删除数目的不同关系导出相应的度分布和幂率指数的表达式。理论、数值分析和模拟结果表明:该模型能自组织演化成无标度网络,度分布遵循幂率分布,与现实中的一些网络相吻合,由于不确定性的普遍性,该模型具有一般性。

The evolving networks which use uncertainty theory is considered. Based on BA model, we investigate the uncertainty scale-free network which is better to describe the reality networks. Used Markov chain-based numerical method, the degree distribution and degree exponent are obtained based on the different relationships between the adding and deleting links. It is showed that the model can evolve into scale-free network by self-organized and is identical with some real networks. The model is suited in a general setting through analyzing degree distribution.