Random matrix analysis of spectral properties in directed complex networks

By using non-Hermitian random matrix theory, the spectra of adjacency matrices of directed complex networks are analyzed. Both the short-range and long-range correlations in the eigenvalues are numerically calculated for typical directed complex networks and compared with the predictions of Ginibre's Ensemble. The spectral density ρ(λ), the nearest neighbor spacing distribution p(s) and the number variance Σ²(L) show good agreements with Ginibre's ensemble when the adjacency matrices of directed complex networks are in the strongly non-Hermitian regime. Therefore, non-Hermitian random matrix theory provides a new way to model and study the spectral properties of directed complex networks.