| Full text | |
| Author(s): |
Peron, Thomas
;
de Resende, Bruno Messias F.
;
Rodrigues, Francisco A.
;
Costa, Luciano da F.
;
Mendez-Bermudez, J. A.
Total Authors: 5
|
| Document type: | Journal article |
| Source: | PHYSICAL REVIEW E; v. 102, n. 6, p. 9-pg., 2020-12-10. |
| 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, 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: | 19/06931-2 - Random matrix theory approach to complex networks |
| Grantee: | Francisco Aparecido Rodrigues |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| FAPESP's process: | 16/25682-5 - Information spreading in complex networks |
| Grantee: | Francisco Aparecido Rodrigues |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 16/23827-6 - Analysis of epidemic and synchronization processes in complex networks |
| Grantee: | Thomas Kaue Dal Maso Peron |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |
| FAPESP's process: | 15/22308-2 - Intermediate representations in Computational Science for knowledge discovery |
| Grantee: | Roberto Marcondes Cesar Junior |
| Support Opportunities: | Research Projects - Thematic Grants |