Universality in the spectral and eigenfunction properties of random networks

Author(s)

Mendez-Bermudez, J. A. ; Alcazar-Lopez, A. ; Martinez-Mendoza, A. J. ; Rodrigues, Francisco A. ; Peron, Thomas K. D. M.

• Document type: Journal article
• Source: PHYSICAL REVIEW E; v. 91, n. 3, p. 10-pg., 2015-03-13.

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 Erdos-Renyi (ER) fully random networks are universal for fixed average degree xi = alpha N (alpha 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 alpha = 0, when the vertices in the network are isolated, to alpha = 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. (AU)

• FAPESP's process: 11/50761-2 - Models and methods of e-Science for life and agricultural sciences
• Grantee: Roberto Marcondes Cesar Junior
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 13/26416-9 - Modelling of dynamical processes in complex networks
• Grantee: Francisco Aparecido Rodrigues
• Support Opportunities: Regular Research Grants
• FAPESP's process: 12/22160-7 - Synchronization of Kuramoto Oscillators in Complex Networks
• Grantee: Thomas Kaue Dal Maso Peron
• Support Opportunities: Scholarships in Brazil - Doctorate