无标度网络拓扑结构非均匀性研究  

Heterogeneity of Scale-free Network Topology

作　　者：吴俊[1] 谭跃进[1] 邓宏钟[1] 朱大智[1] 

机构地区：[1]国防科技大学信息系统与管理学院管理系,长沙410073

出　　处：《系统工程理论与实践》2007年第5期101-105,共5页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(70501032)

摘　　要：利用网络结构熵定量分析了无标度网络拓扑结构的非均匀性.通过引入度秩函数,解析地给出了无标度网络的网络结构熵.研究发现当标度指数大于2时,无标度网络的网络结构熵仅与标度指数有关,与网络规模及最小度无关.在给定网络规模及最小度条件下,无标度网络的网络结构熵在标度指数等于1.7附近取最小值,即此时网络最不均匀,当标度指数大于1.7时,无标度网络的网络结构熵随标度指数单调递增.The heterogeneity of scale-free network topology is studied using network structure entropy （NSE）. NSE of scale-free networks is presented analytically by introducing a degree-rank function. It is shown that NSE of scalefree networks is only dependent of the scaling exponent and independent of the size or the minimum degree of networks when scaling exponent is greater than 2. Given the size and the minimum degree of scale-free networks, it is shown that NSE reached a minimum value when scaling exponent is about equal to 1.7 and then NSE increases with increasing scaling exponent after the minimum value.

关 键 词：无标度网络 非均匀性 度分布 度序列 网络结构熵 

分 类 号：N949[自然科学总论—系统科学]