Normalized entropy of rank distribution： a novel measure of heterogeneity of complex networks  

作　　者：吴俊 谭跃进 邓宏钟 朱大智 

机构地区：[1]Natl Univ Def Technol, Coll Informat Syst & Management, Changsha 410073, Peoples R China

出　　处：《Chinese Physics B》2007年第6期1576-1580,共5页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China （Grant No 70501032）.

摘　　要：Many unique properties of complex networks result from heterogeneity. The measure and analysis of heterogeneity are important and desirable to the research of the properties and functions of complex networks. In this paper, the rank distribution is proposed as a new statistic feature of complex networks. Based on the rank distribution, a novel measure of the heterogeneity called a normalized entropy of rank distribution （NERD） is proposed. The NERD accords with the normal meaning of heterogeneity within the context of complex networks compared with conventional measures. The heterogeneity of scale-free networks is studied using the NERD. It is shown that scale-free networks become more heterogeneous as the scaling exponent decreases and the NERD of scale-free networks is independent of the number of vertices, which indicates that the NERD is a suitable and effective measure of heterogeneity for networks with different sizes.Many unique properties of complex networks result from heterogeneity. The measure and analysis of heterogeneity are important and desirable to the research of the properties and functions of complex networks. In this paper, the rank distribution is proposed as a new statistic feature of complex networks. Based on the rank distribution, a novel measure of the heterogeneity called a normalized entropy of rank distribution （NERD） is proposed. The NERD accords with the normal meaning of heterogeneity within the context of complex networks compared with conventional measures. The heterogeneity of scale-free networks is studied using the NERD. It is shown that scale-free networks become more heterogeneous as the scaling exponent decreases and the NERD of scale-free networks is independent of the number of vertices, which indicates that the NERD is a suitable and effective measure of heterogeneity for networks with different sizes.

关 键 词：complex networks HETEROGENEITY rank distribution scale-free networks 

分 类 号：O233[理学—运筹学与控制论] N941.4[理学—数学]