Spectral analysis of Chinese language: Co-occurrence networks from four literary genres

The eigenvalues and eigenvectors of the adjacency matrix of a network contain essential information about its topology. For each of the Chinese language co-occurrence networks constructed from four literary genres, i.e., essay, popular science article, news report, and novel, it is found that the largest eigenvalue depends on the network size N , the number of edges, the average shortest path length, and the clustering coefficient. Moreover, it is found that their node-degree distributions all follow a power-law. The number of different eigenvalues, N λ , is found numerically to increase in the manner of N λ ∝ log N for novel and N λ ∝ N for the other three literary genres. An “M” shape or a triangle-like distribution appears in their spectral densities. The eigenvector corresponding to the largest eigenvalue is mostly localized to a node with the largest degree. For the above observed phenomena, mathematical analysis is provided with interpretation from a linguistic perspective.