Normal mode analysis of spectra of random networks

Autor(es)

Torres-Vargas, G. ^{[1, 2]} ; Fossion, R. ^{[3, 4]} ; Mendez-Bermudez, J. A. ^[5]

Afiliação do(s) autor(es)

^[1] Univ Autonoma Estado Hidalgo, Inst Ciencias Basicas & Ingn, Pachuca 42184, Hidalgo - Mexico

^[2] Univ Autonoma Metropolitana Cuajimalpa, Posgrad Ciencias Nat & Ingn, Cd De Mexico 05348 - Mexico

^[3] Univ Nacl Autonoma Mexico, Inst Ciencias Nucl, Cd De Mexico 04510 - Mexico

^[4] Univ Nacl Autonoma Mexico, Ctr Ciencias Complejidad, Cd De Mexico 04510 - Mexico

^[5] Benemerita Univ Autonoma Puebla, Inst Fis, Apartado Postal J-18, Puebla 72570 - Mexico

• Tipo de documento: Artigo Científico
• Fonte: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS; v. 545, MAY 1 2020.
• Citações Web of Science: 1

Resumo

Several spectral fluctuation measures of random matrix theory (RMT) have been applied in the study of spectral properties of networks. However, the calculation of those statistics requires performing an unfolding procedure, which may not be an easy task. In this work, network spectra are interpreted as time series, and we show how their short and long-range correlations can be characterized without implementing any previous unfolding. In particular, we consider three different representations of Erdos-Renyi (ER) random networks: standard ER networks, ER networks with random-weighted self-edges, and fully random-weighted ER networks. In each case, we apply singular value decomposition (SVD) such that the spectra are decomposed in trend and fluctuation normal modes. We obtain that the fluctuation modes exhibit a clear crossover between the Poisson and the Gaussian orthogonal ensemble statistics when the average degree of ER networks changes. Moreover, by using the trend modes, we perform a data-adaptive unfolding to calculate, for comparison purposes, traditional fluctuation measures such as the nearest neighbor spacing distribution, number variance Sigma(2), as well as Delta(3) and delta(n) statistics. The thorough comparison of RMT short and long-range correlation measures make us identify the SVD method as a robust tool for characterizing random network spectra. (C) 2019 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 19/06931-2 - Métodos de matrizes aleatórias em redes complexas
• Beneficiário: Francisco Aparecido Rodrigues
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional