Volume 87, Number 4, August 2009
Article Number 48010
Number of page(s) 5
Section Interdisciplinary Physics and Related Areas of Science and Technology
Published online 15 September 2009
EPL, 87 (2009) 48010
DOI: 10.1209/0295-5075/87/48010

Randomness of random networks: A random matrix analysis

S. Jalan and J. N. Bandyopadhyay

Max-Planck Institute for the Physics of Complex Systems - Nöthnitzerstr. 38, D-01187 Dresden, Germany, EU

received 18 March 2009; accepted in final form 7 August 2009; published August 2009
published online 15 September 2009

We analyze complex networks under the random matrix theory framework. Particularly, we show that $\Delta _{3}$ statistics, which gives information about the long-range correlations among eigenvalues, provides a measure of randomness in networks. As networks deviate from the regular structure, $\Delta _{3}$ follows the random matrix prediction of logarithmic behavior (i.e., $\Delta_3(L) \sim \frac{1}{\pi^2} \ln L
$) for longer scale.

89.75.Hc - Networks and genealogical trees.
89.90.+n - Other topics in areas of applied and interdisciplinary physics.

© EPLA 2009