Spectral transitions in networks
| dc.creator | Palla, Gergely | |
| dc.creator | Vattay, Gabor | |
| dc.date | 2007-01-04 | |
| dc.date.accessioned | 2026-07-07T07:38:37Z | |
| dc.date.available | 2026-07-07T07:38:37Z | |
| dc.description | We study the level spacing distribution p(s) in the spectrum of random networks. According to our numerical results, the shape of p(s) in the Erdos-Renyi (E-R) random graph is determined by the average degree <k>, and p(s) undergoes a dramatic change when <k> is varied around the critical point of the percolation transition, <k>=1. When <k> > 1, the p(s) is described by the statistics of the Gaussian Orthogonal Ensemble (GOE), one of the major statistical ensembles in Random Matrix Theory, whereas at <k>=1 it follows the Poisson level spacing distribution. Closely above the critical point, p(s) can be described in terms of an intermediate distribution between Poisson and the GOE, the Brody-distribution. Furthermore, below the critical point p(s) can be given with the help of the regularised Gamma-function. Motivated by these results, we analyse the behaviour of p(s) in real networks such as the Internet, a word association network and a protein protein interaction network as well. When the giant component of these networks is destroyed in a node deletion process simulating the networks subjected to intentional attack, their level spacing distribution undergoes a similar transition to that of the E-R graph. | |
| dc.description | 11 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/physics/0701054 | |
| dc.identifier | http://arxiv.org/abs/physics/0701054 | |
| dc.identifier | New J. Phys. 8 307 (2006) | |
| dc.identifier | doi:10.1088/1367-2630/8/12/307 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121155 | |
| dc.subject | Data Analysis, Statistics and Probability | |
| dc.subject | Biological Physics | |
| dc.title | Spectral transitions in networks | |
| dc.type | text |