Weighted random-geometric and random-rectangular graphs: spectral and eigenfunction properties of the adjacency matrix

Alonso, L. ; Mendez-Bermudez, J.A. ; Gonzalez-Melendrez, A. ; Moreno, Y. (Universidad de Zaragoza)

Resumen: Within a random-matrix theory approach, we use the nearest-neighbour energy-level spacing distribution P(s) and the entropic eigenfunction localization length l to study spectral and eigenfunction properties (of adjacency matrices) of weighted random-geometric and random-rectangular graphs. A random-geometric graph (RGG) considers a set of vertices uniformly and independently distributed on the unit square, while for a random-rectangular graph (RRG) the embedding geometry is a rectangle. The RRG model depends on three parameters: The rectangle side lengths a and 1/a, the connection radius r and the number of vertices N. We then study in detail the case a = 1, which corresponds to weighted RGGs and explore weighted RRGs characterized by a similar to 1, that is, two-dimensional geometries, but also approach the limit of quasi-one-dimensional wires when a >> 1. In general, we look for the scaling properties of P(s) and l as a function of a, r and N. We find that the ratio r/N-gamma, with gamma (a) approximate to -1/2, fixes the properties of both RGGs and RRGs. Moreover, when a >= 10 we show that spectral and eigenfunction properties of weighted RRGs are universal for the fixed ratio r/CN gamma, with C(a) approximate to a.

Idioma: Inglés

DOI: 10.1093/comnet/cnx053

Año: 2018

Publicado en: JOURNAL OF COMPLEX NETWORKS 6, 5 (2018), 753-766
ISSN: 2051-1310

Factor impacto SCIMAGO: 0.608 - Applied Mathematics (Q1) - Computational Mathematics (Q1) - Management Science and Operations Research (Q1) - Control and Optimization (Q1) - Computer Networks and Communications (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA/FENOL-GROUP
Financiación: info:eu-repo/grantAgreement/ES/MINECO/FIS2014-55867-P

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Física Teórica (Dpto. Física Teórica)