有向复杂网络的Poisson模型

Poisson model of directed complex networks

考虑了节点到达过程是Poisson过程的有向复杂网络.本文研究了这类网络的瞬态度分布和稳态平均度分布.利用Poisson过程理论对这类网络进行了分析,获得了度分布的解析表达式.结果表明,虽然这类网络的稳态平均入度和稳态平均出度分布与节点的到达过程无关,但瞬态入度和出度分布依赖于节点的到达过程.

The BA model is a famous model for the undirected networks. Unfortunately, the analysis by Barabási et al on the model is incorrect. The goal of the present paper is to propose Poisson growth directed networks in which the nodes arrival process is a Poisson process. The Poisson directed model describes real networks better than the BA model, for example, WWW network and phone call network. The degree distribution and stationary average degree distribution of the model are investigated. The Poisson process theory is introduced, that allows us to predict the dynamics of individual nodes in the system, and to calculate analytically the connectivity distribution. Although the stationary average indegree and out-degree distributions of the model are independent of the arrival process of nodes, the transient in-degree and out-degree distributions are dependent on the arrival process.