摘要
复杂网络的Laplacian矩阵的特征值和特征向量包含了其拓扑和集体行为等重要信息.该文研究了演化的汉语语言网络的Laplacian矩阵的谱密度、谱排序和特征向量等.研究发现特征值集中分布在区间[0,3]上,并且随着网络规模的增加,[0,3]上的谱密度之和逐渐减小;如果将特征值按降序排列,那么排在最前面的特征值及其序号之间满足幂律分布,其它较大的特征值与中间部分的特征值则满足指数分布;网络的度与前三大特征值对应的特征向量有关,但两者的变化趋势又不尽相同.此外,还将上述结论与邻接矩阵的结果进行了比较.
The eigenvalues and eigenvectors of Laplacian matrix of a complex network contain information about its topology and collective behavior.In this paper,for the evolving Chinese linguistic networks,spectral density,spectral order,and eigenvectors of their Laplacian matrices are studied.Interestingly,the spectra concentrate on the interva[0,3],and the sum of spectral density on[0,3]decreases successively with the expansion of network size.If the eigenvalues are listed in decreasing order,then the top eigenvalues follow a power-law distribution,while the other top eigenvalues and the middle part satisfy exponential distributions.The change trend of the degrees and the eigenvectors corresponding to the top three eigenvalues is variety.Moreover,these results are compared with those of the adjacency matrices.
作者
张子涵
梁伟
ZHANG Zihan;LIANG Wei(School of Mathematics and Information Science, Henan Polytechnic University,Jiaozuo, Henan 454003, China)
出处
《华中师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2021年第6期1013-1019,共7页
Journal of Central China Normal University：Natural Sciences
基金
国家自然科学基金青年项目(61403126)
河南省教育厅科技研究重点项(15A120010).
关键词
汉语
同现网络
谱分析
LAPLACIAN矩阵
Chinese language
co-occurrence network
spectral analysis
Laplacian matrix
