度分布为正态分布的复杂网络度序列长度的研究与分析

Research and Analysis of the Length of Degree Sequence of Complex Network of Normal Distribution

度分布是复杂网络模型的重要特征.针对度分布符合指数分布、幂律分布和扩展幂律分布的复杂网络模型,笔者所在课题组前期的研究结果表明节点度序列(1≤k_1<k_2<…<k_l)长度l是log_2N级别的(N为网络节点数);在前期研究所得结论的基础上,文中针对度分布符合正态分布的复杂网络模型,从理论的角度证明了度序列长度l也是log2N级别的;并选取ER随机网络进行仿真实验,仿真实验表明,度序列的长度是级别的;最后对大量的现实网络模型进行了验证,结果表明现实网络的度序列长度l也是与log_2N同一级别.

Degree distribution is an important characteristic of complex network.Aiming at the complex network model of degree distribution in congruity with exponential,power law and extended power law distributions,the previous research results of our project team show that the length l of vertex-degree sequence(1≤k 1<k 2<…<k l)of complex network is of order log 2 N(N is the number of network nodes).Based on the conclusions of the previous studies,this paper proves that the degree sequence length l is also is of order log 2 N from the theoretical point of view for the complex network model that the degree distribution meets the normal distribution.The simulation experiment shows that the length l of the degree sequence is of order log 2 N by selecting ER random network.Finally,a large number of real network models are verified,and the results show that the length of the real network degree sequence is also at the same level as log 2 N.