75905 20191212102143.0 doi 10.1093/comnet/cnx053 sideral 108441 ART-2018-108441 eng Alonso, L. Weighted random-geometric and random-rectangular graphs: spectral and eigenfunction properties of the adjacency matrix 2018 Access copy available to the general public Unrestricted 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. info:eu-repo/grantAgreement/ES/DGA/FENOL-GROUP info:eu-repo/grantAgreement/ES/MINECO/FIS2014-55867-P info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 0.608 2018 Applied Mathematics 2018 Q1 Computational Mathematics 2018 Q1 Management Science and Operations Research 2018 Q1 Control and Optimization 2018 Q1 Computer Networks and Communications 2018 Q1 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Mendez-Bermudez, J.A. Gonzalez-Melendrez, A. (orcid)0000-0002-0895-1893 Moreno, Y. Universidad de Zaragoza 2004 405 Universidad de Zaragoza Dpto. Física Teórica Área Física Teórica 6, 5 (2018), 753-766 J. complex. netw JOURNAL OF COMPLEX NETWORKS 2051-1310 1728436 http://zaguan.unizar.es/record/75905/files/texto_completo.pdf Postprint 127147 http://zaguan.unizar.es/record/75905/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:75905 articulos driver 2019-12-12-10:13:45 ARTICLE