中国物理B ›› 2007, Vol. 16 ›› Issue (6): 1576-1580.doi: 10.1088/1009-1963/16/6/014

• GENERAL • 上一篇    下一篇

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

吴俊, 谭跃进, 邓宏钟, 朱大智   

  1. College of Information Systems and Management, National University of Defense Technology, Changsha 410073, China
  • 收稿日期:2006-09-28 修回日期:2006-11-14 出版日期:2007-06-20 发布日期:2007-06-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 70501032).

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

Wu Jun(吴俊)†, Tan Yue-Jin(谭跃进), Deng Hong-Zhong(邓宏钟), and Zhu Da-Zhi(朱大智)   

  1. College of Information Systems and Management, National University of Defense Technology, Changsha 410073, China
  • Received:2006-09-28 Revised:2006-11-14 Online:2007-06-20 Published:2007-06-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 70501032).

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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.

Abstract: 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.

Key words: complex networks, heterogeneity, rank distribution, scale-free networks

中图分类号:  (Thermodynamic functions and equations of state)

  • 05.70.Ce
02.50.Ng (Distribution theory and Monte Carlo studies) 05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion) 89.75.Hc (Networks and genealogical trees)