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• W3080148029 abstract "Previous literature on random matrix and network science has traditionally employed measures derived from nearest-neighbor level spacing distributions to characterize the eigenvalue statistics of random matrices. This approach, however, depends crucially on eigenvalue unfolding procedures, which in many situations represent a major hindrance due to constraints in the calculation, specially in the case of complex spectra. Here we study the spectra of directed networks using the recently introduced ratios between nearest- and next-to-nearest eigenvalue spacing, thus circumventing the shortcomings imposed by spectral unfolding. Specifically, we characterize the eigenvalue statistics of directed ErdH{o}s-R'enyi (ER) random networks by means of two adjacency matrix representations; namely (i) weighted non-Hermitian random matrices and (ii) a transformation on non-Hermitian adjacency matrices which produces weighted Hermitian matrices. For both representations, we find that the distribution of spacing ratios becomes universal for a fixed average degree, in accordance with undirected random networks. Furthermore, by calculating the average spacing ratio as a function of the average degree, we show that the spectral statistics of directed ER random networks undergoes a transition from Poisson to Ginibre statistics for model (i) and from Poisson to Gaussian Unitary Ensemble statistics for model (ii). Eigenvector delocalization effects of directed networks are also discussed." @default.
• W3080148029 created "2020-09-01" @default.
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• W3080148029 date "2020-12-10" @default.
• W3080148029 modified "2023-10-17" @default.
• W3080148029 title "Spacing ratio characterization of the spectra of directed random networks" @default.
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• W3080148029 doi "https://doi.org/10.1103/physreve.102.062305" @default.
• W3080148029 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/33465954" @default.
• W3080148029 hasPublicationYear "2020" @default.
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