Adjacency spectra of Chinese character co-occurrence networks in different historical periods

The spectrum of a network provides important information about its global structure. For Chinese character co-occurrence networks constructed from articles published in 11 different historical periods in China, the spectra and eigenvectors of their adjacency matrices are studied. It is found that the middle part of the spectral distribution can be fitted by a line with slope −0.01 in each incorporated network, whereas two segments with the same slope −0.02 are needed for other single networks. If the eigenvalues, λ_i, are listed in decreasing order, then the formers depend on their ranks, i, in the form of λ_i ∝ −β log i, where 1.70 ≤ β ≤ 9.69. In the spectral density ρ(λ), there is a triangle-like shape in each of the incorporated networks, while the ρ(λ) values are nearly symmetrical in each single network. These and other results indicate that the spectra and eigenvectors can provide useful insight into the structural properties of Chinese linguistic networks.