| Normalized entropy of rank distribution： a novel measure of heterogeneity of complex networks |
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| 引用本文： | 吴俊,谭跃进,邓宏钟,朱大智. Normalized entropy of rank distribution： a novel measure of heterogeneity of complex networks[J]. 中国物理, 2007, 16(6): 1576-1580. DOI: 10.1088/1009-1963/16/6/014 |
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| 作者姓名： | 吴俊 谭跃进 邓宏钟 朱大智 |
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| 作者单位： | College of Information Systems and Management, NationalUniversity of Defense Technology, Changsha 410073, China |
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| 基金项目： | Project supported by the NationalNatural 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 areimportant and desirable to the research of the properties andfunctions of complex networks. In this paper, the rank distributionis proposed as a new statistic feature of complex networks. Based onthe rank distribution, a novel measure of the heterogeneity called anormalized entropy of rank distribution (NERD) is proposed. The NERDaccords with the normal meaning of heterogeneity within the contextof complex networks compared with conventional measures. Theheterogeneity of scale-free networks is studied using the NERD. Itis shown that scale-free networks become more heterogeneous as thescaling exponent decreases and the NERD of scale-free networks isindependent of the number of vertices, which indicates that the NERDis a suitable and effective measure of heterogeneity for networkswith different sizes.
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| 关 键 词： | 复杂网络 异质性 正规化熵 等级分布 |
| 收稿时间： | 2006-09-28 |
| 修稿时间： | 2006-09-282006-11-14 |
Normalized entropy of rank distribution: a novel measure of heterogeneity of complex networks |
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| Wu Jun,Tan Yue-Jin,Deng Hong-Zhong and Zhu Da-Zhi. Normalized entropy of rank distribution: a novel measure of heterogeneity of complex networks[J]. Chinese Physics, 2007, 16(6): 1576-1580. DOI: 10.1088/1009-1963/16/6/014 |
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| Authors: | Wu Jun Tan Yue-Jin Deng Hong-Zhong Zhu Da-Zhi |
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| Affiliation: | College of Information Systems and Management, National University of Defense Technology, Changsha 410073, China |
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| Abstract: | Many unique properties of complex networks result from heterogeneity. The measure and analysis of heterogeneity areimportant and desirable to the research of the properties andfunctions of complex networks. In this paper, the rank distributionis proposed as a new statistic feature of complex networks. Based onthe rank distribution, a novel measure of the heterogeneity called anormalized entropy of rank distribution (NERD) is proposed. The NERDaccords with the normal meaning of heterogeneity within the contextof complex networks compared with conventional measures. Theheterogeneity of scale-free networks is studied using the NERD. Itis shown that scale-free networks become more heterogeneous as thescaling exponent decreases and the NERD of scale-free networks isindependent of the number of vertices, which indicates that the NERDis a suitable and effective measure of heterogeneity for networkswith different sizes. |
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| Keywords: | complex networks heterogeneity rank distribution scale-free networks |
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