网络维数:一种度量复杂网络的新方法  

Network Dimension:A New Measure for Complex Networks

作　　者：刘胜久[1,2] 李天瑞 刘小伟[3] LIU Sheng-jiu;LI Tian-rui;LIU Xiao-wei(School of Information Science and Technology,Southwest Jiaotong University,Chengdu 611756,China;Sichuan Key Lab of Cloud Computing and Intelligent Technique,Chengdu 611756,China;Department of Mathematics and Computer Science,Nanchang Normal University,Nanchang 330032,China)

机构地区：[1]西南交通大学信息科学与技术学院,成都611756 [2]四川省云计算与智能技术高校重点实验室,成都611756 [3]南昌师范学院数学与计算机科学系,南昌330032

出　　处：《计算机科学》2019年第1期51-56,共6页Computer Science

基　　金：国家自然科学基金项目(61573292;61262058;61562063);江西省教育厅科技项目(GJJ171109;GJJ161241)资助

摘　　要：如何对复杂网络进行刻画与度量,一直是人们关注的热点。在研究自相似复杂网络分形维数的基础上,提出了一种度量复杂网络的新方法——网络维数,即复杂网络边权重和的对数值与节点权重和的对数值的比值,可以将边权重及点权重推广到实数域和复数域;同时给出了不同类型权重对应的网络维数的计算方法;最后以几个代表性的经典复杂网络模型为例,讨论了所提出的网络维数的若干性质。How to measure complex networks has always received much attention.This paper proposed a new method based on the analysis of fractal dimension of self-similarity complex networks,named network dimension,to measure complex networks.Network dimension is expressed as the division of logarithm of the sum of edges’weights and logarithm of the sum of nodes’weights of complex networks.The weights of both edge and node are extended to real and complex number fields.The calculation methods of network dimensions of weighted networks with different types of weights were presented.Finally,several representative classical complex network models were taken as examples to discuss some properties of the proposed network dimension.

关 键 词：复杂网络 自相似网络 分形维数 网络维数 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]