# 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…

## 28 Citations

Information Entropy of Tight-Binding Random Networks with Losses and Gain: Scaling and Universality

- Mathematics, MedicineEntropy
- 2019

It is demonstrated that for fixed ξ, the spectral properties (characterized by the position of the eigenvalues on the complex plane) of the network model are also universal; i.e., they do not depend on the specific values of thenetwork parameters.

Normal mode analysis of spectra of random networks

- Mathematics, Physics
- 2020

Abstract Several spectral fluctuation measures of random matrix theory (RMT) have been applied in the study of spectral properties of networks. However, the calculation of those statistics requires…

Scaling properties of multilayer random networks.

- Mathematics, MedicinePhysical review. E
- 2017

It is numerically demonstrated that the normalized localization length β of the eigenfunctions of multilayer random networks follows a simple scaling law given by β=x=x/(1+x^{*}), with x=γ(b_{eff}^{2}/L)^{δ}, δ∼1, and b_{EFF} being the effective bandwidth of the adjacency matrix of the network, whose size is L.

Multifractality in random networks with power-law decaying bond strengths.

- Physics, MedicinePhysical review. E
- 2019

In this paper we demonstrate numerically that random networks whose adjacency matrices A are represented by a diluted version of the power-law banded random matrix (PBRM) model have multifractal…

Spectral statistics of random geometric graphs

- Mathematics, Physics
- 2016

We study the spectrum of random geometric graphs using random matrix theory. We look at short range correlations in the level spacings via the nearest neighbour and next nearest neighbour spacing…

Geometrical and spectral study of β-skeleton graphs.

- Mathematics, PhysicsPhysical review. E
- 2019

An extensive numerical analysis of β-skeleton graphs is performed and it is concluded that a localization transition occurs at β=1, and spectral and eigenvector properties of random BSGs are explored by the use of the nearest-neighbor energy-level spacing distribution and the entropic eigen vector localization length.

Random matrix analysis of multiplex networks

- PhysicsPhysica A: Statistical Mechanics and its Applications
- 2021

We investigate the spectra of adjacency matrices of multiplex networks under random matrix theory (RMT) framework. Through extensive numerical experiments, we demonstrate that upon multiplexing two…

Computational Properties of General Indices on Random Networks

- Computer Science, MathematicsSymmetry
- 2020

A step forward is given in the scaling of topological indices since a scaling law is found that covers different network models and it is proposed to establish their statistical analysis as a generic tool for studying average properties of random networks.

Diluted banded random matrices: scaling behavior of eigenfunction and spectral properties

- Physics, Mathematics
- 2017

We demonstrate that the normalized localization length β of the eigenfunctions of diluted (sparse) banded random matrices follows the scaling law . The scaling parameter of the model is defined as ,…

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

- Computer Science, MathematicsJ. Complex Networks
- 2018

The ratio $r/N^\gamma', with $\gamma(a))\approx -1/2$, fixes the properties of both RGGs and RRGs, and it is shown that spectral and eigenfunction properties of weighted RRGs are universal for the fixed ratio.

## References

SHOWING 1-10 OF 69 REFERENCES

Quantum signatures of chaos

- Physics
- 1991

The distinction between level clustering and level repulsion is one of the quantum analogues of the classical distinction between globally regular and predominantly chaotic motion (see Figs. 1, 2,…

Mesoscopic phenomena in solids

- Physics
- 1991

Preface. 1. Aharonov-Bohm effects in loops of gold (S. Washburn). 2. Mesoscopic fluctuations of current density in disordered conductors (B.Z. Spivak and A.Yu. Zyuzin). 3. Interference, fluctuations…

Rev

- Mod. Phys. 74, 47
- 2002

Nucl

- Phys. A 687, 405
- 2001

Networks: An introduction (Oxford

- 2010

New J

- Phys. 8, 307
- 2006

Random matrices (Elsevier

- 2004

Random matrices (Elsevier, Amsterdam

- 2004

Phys

- Rev. B 37, 3557
- 1988

Publications of the Mathematical Institute of the Hungarian Academy of Sciences 5

- 17 (1960); Acta Mathematica Scientia Hungary 12, 261
- 1961