000075905 001__ 75905
000075905 005__ 20191212102143.0
000075905 0247_ $$2doi$$a10.1093/comnet/cnx053
000075905 0248_ $$2sideral$$a108441
000075905 037__ $$aART-2018-108441
000075905 041__ $$aeng
000075905 100__ $$aAlonso, L.
000075905 245__ $$aWeighted random-geometric and random-rectangular graphs: spectral and eigenfunction properties of the adjacency matrix
000075905 260__ $$c2018
000075905 5060_ $$aAccess copy available to the general public$$fUnrestricted
000075905 5203_ $$aWithin 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.
000075905 536__ $$9info:eu-repo/grantAgreement/ES/DGA/FENOL-GROUP$$9info:eu-repo/grantAgreement/ES/MINECO/FIS2014-55867-P
000075905 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000075905 592__ $$a0.608$$b2018
000075905 593__ $$aApplied Mathematics$$c2018$$dQ1
000075905 593__ $$aComputational Mathematics$$c2018$$dQ1
000075905 593__ $$aManagement Science and Operations Research$$c2018$$dQ1
000075905 593__ $$aControl and Optimization$$c2018$$dQ1
000075905 593__ $$aComputer Networks and Communications$$c2018$$dQ1
000075905 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000075905 700__ $$aMendez-Bermudez, J.A.
000075905 700__ $$aGonzalez-Melendrez, A.
000075905 700__ $$0(orcid)0000-0002-0895-1893$$aMoreno, Y.$$uUniversidad de Zaragoza
000075905 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica
000075905 773__ $$g6, 5 (2018), 753-766$$pJ. complex. netw$$tJOURNAL OF COMPLEX NETWORKS$$x2051-1310
000075905 8564_ $$s1728436$$uhttps://zaguan.unizar.es/record/75905/files/texto_completo.pdf$$yPostprint
000075905 8564_ $$s127147$$uhttps://zaguan.unizar.es/record/75905/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000075905 909CO $$ooai:zaguan.unizar.es:75905$$particulos$$pdriver
000075905 951__ $$a2019-12-12-10:13:45
000075905 980__ $$aARTICLE