演化的汉语同现网络的Laplacian谱分析

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.

Laplacian spectra of evolving Chinese linguistic co-occurrence networks

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.