增长网络的形成机理和度分布计算

The Mechanisms and Degree Distributions of Growing Networks

关于增长网络的形成机理,着重介绍由线性增长与择优连接组成的BA模型, 以及加速增长模型.此外,我们提出了一个含反择优概率删除旧连线的模型,这个模型能自组织演化成scale-free(SF)网络.关于计算SF网络的度分布,简要介绍文献上常用的基于连续性理论的动力学方法(包括平均场和率方程)和基于概率理论的主方程方法.另外,我们基于马尔可夫链理论还首次尝试了数值计算方法.这一方法避免了复杂方程的求解困难,所以较有普适性,因此可用于研究更为复杂的网络模型.我们用这种数值计算方法研究了一个具有对数增长的加速增长模型,这个模型也能自组织演化成SF网络.

In present paper, we summarize the growing and preferential mechanisms of BA model and the accelerating growth models. We introduce a growing model with the anti-preferential deletion, this system can self-organize a scale-free network. We summarize the Mean-field method, Master-equation and Rate-equation method of calculating degree distributions. We introduce a new numerical method by Markov chains. It can study more complicated models of growing networks. We study a accelerating growth network by Markov method, the system can self-organize a scale-free network.