title: Universality in the spectral and eigenfunction properties of random networks.
abstract: By the use of extensive numerical simulations, we show that the nearest-neighbor energy-level spacing distribution P(s) and the entropic eigenfunction localization length of the adjacency matrices of Erdős-Rényi (ER) fully random networks are universal for fixed average degree ξ≡αN (α and N being the average network connectivity and the network size, respectively). We also demonstrate that the Brody distribution characterizes well P(s) in the transition from α=0, when the vertices in the network are isolated, to α=1, when the network is fully connected. Moreover, we explore the validity of our findings when relaxing the randomness of our network model and show that, in contrast to standard ER networks, ER networks with diagonal disorder also show universality. Finally, we also discuss the spectral and eigenfunction properties of small-world networks.
authors: Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico.
authors: J A
authors: JA
authors: Méndez-Bermúdez
authors: Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico.
authors: A
authors: A
authors: Alcazar-López
authors: Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico and Elméleti Fizika Tanszék, Fizikai Intézet, Budapesti Műszaki és Gazdaságtudományi Egyetem, H-1521 Budapest, Hungary.
authors: A J
authors: AJ
authors: Martínez-Mendoza
authors: Departamento de Matemática Aplicada e Estatística, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668,13560-970 São Carlos, São Paulo, Brazil.
authors: Francisco A
authors: FA
authors: Rodrigues
authors: Instituto de Física de São Carlos, Universidade de São Paulo, CP 369, 13560-970, São Carlos, São Paulo, Brazil.
authors: Thomas K Dm
authors: TK
authors: Peron