Geometrical and spectral study of beta-skeleton graphs

Autor(es)

Alonso, L. ; Mendez-Bermudez, J. A. ; Estrada, Ernesto

• Tipo de documento: Artigo Científico
• Fonte: PHYSICAL REVIEW E; v. 100, n. 6, p. 8-pg., 2019-12-19.

Resumo

We perform an extensive numerical analysis of beta-skeleton graphs, a particular type of proximity graphs. In beta-skeleton graph (BSG) two vertices are connected if a proximity rule, that depends of the parameter beta is an element of (0, infinity), is satisfied. Moreover, for beta > 1 there exist two different proximity rules, leading to lune-based and circle-based BSGs. First, by computing the average degree of large ensembles of BSGs we detect differences, which increase with the increase of beta, between lune-based and circle-based BSGs. Then, within a random matrix theory (RMT) approach, we explore spectral and eigenvector properties of random BSGs by the use of the nearest-neighbor energy-level spacing distribution and the entropic eigenvector localization length, respectively. The RMT analysis allows us to conclude that a localization transition occurs at beta = 1. (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