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%.
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 max-ranking is 0. 11%. Meanwhile, by the ARE of frequency-ranking is 5.51%.
出处
《系统工程》
CSCD
北大核心
2006年第5期122-126,共5页
Systems Engineering
基金
国家统计局重点资助项目(LX2005-20)
关键词
复杂网络
幂律
频数法
最大等级法
平均相对误差
Complex Network
Power-law
Frequency-ranking
Max-Ranking
Average-Relative-Error
