增长及非增长无标度网络的成因解析

Cause Analysis of Growing and Non-growing Scale-free Networks

分析两类无标度网络的形成原因,提出一个无标度网络演化模型并进行一系列数值实验.基于分析和实验得到推论:只要保持足够低的网络密度,通过基于度的偏好连接就可形成长期稳定的无标度网络.规模增长和点边增删既是客观存在,又起到了控制网络密度的作用,足够低的网络密度和基于度的偏好连接是所有无标度网络共同的必要条件.推论可同时解释增长和非增长无标度网络的形成原因.研究结果有助于理解各种真实无标度网络和建立相应的模型.

Causes of two classes of scale-free networks are analyzed. A scale-free network evolution model is proposed and a series of numerical experiments are carried out. Theoretical analysis and numerical experiments show that if network density is sparse and stable enough, a persistently stable scale-free network can be produced by degree-based preferential attachment. Growth of network size as well as addition and deletion of vertices and edges are objective realities. They have the function of controlling network density as well. A sufficiently sparse density and degree-based preferential attachment are common necessities of scale-free networks. This deduction can be used to explain reasonably the cause of growing and non-growing scale-free networks. The results are helpful in understanding diversified real scale-free networks and design of corresponding models.