Universality in the spectral and eigenfunction properties of random networks.

@article{MndezBermdez2015UniversalityIT,
  title={Universality in the spectral and eigenfunction properties of random networks.},
  author={J. A. M{\'e}ndez-Berm{\'u}dez and A. Alc{\'a}zar-L{\'o}pez and A. J. Martinez-Mendoza and Francisco Aparecido Rodrigues and Thomas K. D. M. Peron},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2015},
  volume={91 3},
  pages={
          032122
        }
}
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… 

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