Spectra of English evolving word co-occurrence networks

Abstract

Abstract Spectral analysis is a powerful tool that provides global measures of the network properties. In this paper, 200 English articles are collected. A word co-occurrence network is constructed from each single article (denoted by single network). Furthermore, 5 large English word co-occurrence networks are constructed (denoted by large network). Spectra of their adjacency matrices are computed. The largest eigenvalue, λ 1 , depends on the network size N and the number of edges E as λ 1 ∝ N 0.66 and λ 1 ∝ E 0.54 , respectively. The number of different eigenvalues, N λ , increase in the manner of N λ ∝ N 0.58 and N λ ∝ E 0.47 . The middle part of the spectral distribution can be fitted by a line with slope − 0.01 in each of the large networks, whereas two segments with the same slope − 0.03 for 0 ≪ N 260 and − 0.02 for 260 N 2800 are needed for the single networks. An “M”-shape distribution appears in each of the spectral densities of the large networks. These and other results can provide useful insight into the structural properties of English linguistic networks.