复杂网络幂律函数标度指数的估计与检验

The Estimation and Test for Scaling Exponents of Power-Law Functions for Complex Networks

针对度分布以及群规模分布的幂律函数,提出了基于最大似然估计的幂律分布的标度指数估计方法;针对幂律形式的层次聚集函数的标度指数估计,则采用了构建方程组的方法.此外,还引入KS检验统计量和欧几里得距离来检验新方法的估计效果.最后,通过CNN模型网络和爵士音乐家网络两个应用例,证实了新方法对3种标度指数的估计效果均好于图形方法.

New methods were presented to estimate and test the scaling exponents of power-law functions that are universal in the research of structural properties of complex networks. Concretely, a new method based on the maximum likelihood estimation was introduced to estimate the scaling exponents of power-law distributions including degree distribution and community size distribution. For the estimation of the scaling exponent of power-law hierarchical clustering function, a new method was developed by constructing equations group. Meanwhile, KS test statistics and Euclidean distance were introduced to test the performance of new methods. The new methods were verified to have higher performance than graphical methods by two application examples of CNN model-generated network and jazz musician network.