演化网络的拓扑结构

Topology of the Evolution Network

介绍了两种网络模型——进化网络和退化网络,给出了它们度分布主方程的微分形式和解析解,得到度分布p(k,t)的解是随时间演化的,并求得其标度值y.在给定的时间内方程解中的一项呈幂率衰减,另一项反映了尺度效应.当c等于零,时间无限大时得到的度分布解的形式与BA网络的形式相似.

For the developing and decaying network, a kind of model is proposed in this paper. It is given the differential format of master equation of degree distribution and its analytical solution. The obtained result P （ k, t ） is the time evolution of degree distribution and its scale y. At given finite time, one term decays exponentially, the other reflects size effect. For the case of c is equal to zero, the degree distribution is the similar as that of BA network at infinite time.