Spectra of English evolving word co-occurrence networks

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, λ1, depends on the network size N and the number of edges E as λ1∝N0.66 and λ1∝E0.54, respectively. The number of different eigenvalues, Nλ, increase in the manner of Nλ∝N0.58 and Nλ∝E0.47. 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