| 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 B,2007,16(6):1576-1580. |
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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, National
University of Defense Technology, Changsha 410073, China |
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| 基金项目： | 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.
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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 B,2007,16(6):1576-1580. |
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| Authors: | Wu Jun Tan Yue-Jin Deng Hong-Zhong and Zhu Da-Zhi |
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| Institution: | 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 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. |
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| Keywords: | complex networks heterogeneity rank distribution scale-free networks |
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