基于边数随机增长的扩展无标度网络演化模型研究  

An extended scale-free network evolution model based on random growth of edge number

作　　者：王迪飞 菅利荣[1] 刘思峰[1] 薛琛衍 WANG Difei;JIAN Lirong;LIU Sifeng;XUE Chenyan(College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China;Leihua Electronic Technology Research Institute,Aviation Industry Corporation of China,Wuxi 214063,China)

机构地区：[1]南京航空航天大学经济与管理学院,南京211106 [2]中航工业雷华电子技术研究所,无锡214063

出　　处：《系统工程理论与实践》2022年第5期1327-1344,共18页Systems Engineering-Theory & Practice

基　　金：江苏高校哲学社会科学研究重大项目(2019SJZDA036);江苏省社会科学基金(18EYB015);国家自然科学基金(72071111,71573124)。

摘　　要：经典BA无标度网络演化模型假定所有嵌入节点的初始连边数量均相同,而该假定对于许多真实的演化网络往往显得过于严格.为进一步增强模型的通用性,构建了具有边数随机增长特征,即所有嵌入节点的初始连边数量为独立同分布随机变量序列的扩展无标度网络演化模型(简记为ENRG-BA模型).运用马氏链解析法获得了ENRG-BA模型网络稳态度分布的精确表达式,并从分布的性质与数值模拟两个方面验证了解析结果的正确性.研究结果表明,当所有嵌入节点的初始连边数量均具有有限的期望和方差时,ENRG-BA模型存在网络稳态度分布;当所有嵌入节点的初始连边数量均具有相同的分布参数与相同有限区间长度的定义域时,ENRG-BA模型退化为Degenerate ENRG-BA模型(简记为DENRG-BA模型);当所有嵌入节点的初始连边数量均服从相同参数的单点分布时,DENRG-BA模型进一步退化为BA模型.ENRG-BA模型与DENRGBA模型的网络稳态度分布在大度数处均具有与BA模型网络稳态度分布相同的幂律行为,在小度数处则呈现出BA模型网络稳态度分布所不具备且类型丰富的马头形状,其中部分马头形状与某些实际演化网络的度分布中所具有的头部形状十分接近.最后,通过PNAS案例说明了ENRG-BA模型的有效性.The classic BA scale-free network evolution model assumes that the number of initial edges of all embedded nodes is the same,and this assumption is often too strict for many real evolutionary networks.To further enhance the versatility of the model,an extended scale-free network evolution model(abbreviated as ENRG-BA model) is constructed with the feature of edge number random growth,that is,the initial number of edges of all embedded nodes is a sequence of independently and identically distributed random variables.The Markov chain analytic method is used to obtain the accurate expression of the network’s steady-state degree distribution of the ENRG-BA model,and the correctness of the analytical results is verified from the nature of the distribution and numerical simulation.The results show that when the initial number of edges of all embedded nodes has finite expectations and variances,the ENRG-BA model has a network’s steady-state degree distribution.When the initial number of edges of all embedded nodes has the same distribution parameters and the same domains whose interval length is limited,the ENRGBA model degenerates to the DENRG-BA model.When the initial number of edges of all embedded nodes obeys a one-point distribution of the same parameter,the DENRG-BA model further degenerates to the BA model.The network’s steady-state degree distributions of the ENRG-BA model and DENRG-BA model have the same power-law behavior at large node degrees as that of the BA model,while at the small node degrees,there are many types of horse-head shapes that the BA model does not have,and some of them are very close to the head shapes of some actual evolutionary networks.Finally,the effectiveness of the ENRG-BA model is verified through the PNAS case study.

关 键 词：BA模型 ENRG-BA模型 网络稳态度分布 马头形状 

分 类 号：N94[自然科学总论—系统科学]