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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Spacing ratio characterization of the spectra of directed random networks

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Peron, Thomas [1] ; de Resende, Bruno Messias F. [2] ; Rodrigues, Francisco A. [1] ; Costa, Luciano da F. [2] ; Mendez-Bermudez, J. A. [1, 3]
Total Authors: 5
[1] Univ Sao Paulo, Inst Math & Comp Sci, BR-13566590 Sao Carlos, SP - Brazil
[2] Univ Sao Paulo, Sao Carlos Inst Phys, BR-13566590 Sao Carlos, SP - Brazil
[3] Benemerita Univ Autonoma Puebla, Inst Fis, Apartado Postal J-48, Puebla 72570 - Mexico
Total Affiliations: 3
Document type: Journal article
Source: Physical Review E; v. 102, n. 6 DEC 10 2020.
Web of Science Citations: 2

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, especially 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 Erdos-Renyi (ER) random networks by means of two adjacency matrix representations, namely, (1) weighted non-Hermitian random matrices and (2) 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 1 and from Poisson to Gaussian unitary ensemble statistics for model 2. Eigenvector delocalization effects of directed networks are also discussed. (AU)

FAPESP's process: 16/23827-6 - Analysis of epidemic and synchronization processes in complex networks
Grantee:Thomas Kaue Dal Maso Peron
Support type: Scholarships in Brazil - Post-Doctorate
FAPESP's process: 19/06931-2 - Random matrix theory approach to complex networks
Grantee:Francisco Aparecido Rodrigues
Support type: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 15/22308-2 - Intermediate representations in Computational Science for knowledge discovery
Grantee:Roberto Marcondes Cesar Junior
Support type: Research Projects - Thematic Grants
FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
Grantee:José Alberto Cuminato
Support type: Research Grants - Research, Innovation and Dissemination Centers - RIDC
FAPESP's process: 16/25682-5 - Information spreading in complex networks
Grantee:Francisco Aparecido Rodrigues
Support type: Regular Research Grants