| 用最大等级法测定幂律 |
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| 引用本文： | 孙颖,刘小冬,王羽.用最大等级法测定幂律[J].系统工程,2006,24(5):122-126. |
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| 作者姓名： | 孙颖 刘小冬 王羽 |
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| 作者单位： | 1. 西北工业大学,数学与信息科学系,陕西,西安,710072
2. 西北大学,计算机科学系,陕西,西安,710127 |
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| 摘 要： | 幂律是无标度网络的基础，但它的测定不只是统计节点度的频数那么简单，这种做法可能导致错误的结论，譬如本文图2（A）（B），此外频数法的拟合误差不容忽视。本文设计了一种高精度的方法——最大等级法，并证明它是判定整数型大样本幂律随机量的充要条件。我们以平均相对误差为主要评价指标，在相同条件下比较了多种方法，发现最大等级法的平均相对误差最低，只有0．11％，而频数法却有5．51％．
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| 关 键 词： | 复杂网络 幂律 频数法 最大等级法 平均相对误差 |
| 文章编号： | 1001-4098（2006）05-0122-05 |
| 收稿时间： | 2006-03-12 |
| 修稿时间： | 2006-03-12 |
Power-law Measure by Max-ranking Method |
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| SUN Ying,LIU Xiao-dong,WANG Yu.Power-law Measure by Max-ranking Method[J].Systems Engineering,2006,24(5):122-126. |
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| Authors: | SUN Ying LIU Xiao-dong WANG Yu |
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| Abstract: | Power-law is basis of scale-free networks.Its measurement is so subtle that an imprecise method leads to improper results.For instance,there is an obvious error in the fig2(A) and(B) in this paper;error of frequency-ranking cannot be ignored.In this paper,we design a new accurate method named max-ranking to measure power-law.A sufficient and necessary condition of power-law estimation on occasion of huge integral samples is proved.At last,we compare the Average-Relative-Error by different methods,and found that by the ARE of maxranking is 0.11%.Meanwhile,by the ARE of frequency-ranking is 5.51%. |
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| Keywords: | Complex Network Power-law Frequency-ranking Max-Ranking Average-Relative-Error |
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