摘要
给出了一个新的复杂网络宏观统计特征——度秩函数,并推导出了度秩函数与度分布的数学关系。利用相关系数分别研究了无标度网络及指数网络中度秩函数与度分布的精确性。研究表明当无标度网络的标度指数λ≤3.1时,度秩函数的相关系数比度分布的相关系数高,当无标度网络的标度指数λ>3.1时,度秩函数的相关系数比度分布的相关系数低;同时也表明当指数网络的底数α∈(0,0.2)时,度秩函数的相关系数比度分布的相关系数低,当指数网络的底数α∈[0.2,1)时,度秩函数的相关系数比度分布的相关系数高。
The degree-rank function is proposed as a new statistic characteristic of complex network and the mathematical relationship between degree-rank function and degree distribution is derived.The accuracy of degree-rank function and degree distribution in scale-free networks and exponential networks is studied using correlation coefficient,respectively.It is shown that correlation coefficient of degree-rank function is higher than correlation coefficient of degree distribution when scaling exponent λ≤3.1 and reverse when scaling exponent λ>3.1.It is also shown that correlation coefficient of degree-rank function is lower than correlation coefficient of degree distribution when base α∈(0,0.2) and reverse when base α∈[0.2,1).
出处
《复杂系统与复杂性科学》
EI
CSCD
2006年第4期28-34,共7页
Complex Systems and Complexity Science
基金
国家自然科学基金资助项目(70501032)
关键词
复杂网络
度分布
度秩函数
相关系数
统计特征
complex network
degree distribution
degree-rank function
correlation coefficient
statistic characteristic
