Log-periodic oscillations due to discrete effects in complex networks
Disordered Systems and Neural Networks
2007-06-17 v1 Statistical Mechanics
Abstract
We show that discretization of internode distribution in complex networks affects internode distances l_ij calculated as a function of degrees (k_i k_j) and an average path length <l> as function of network size N. For dense networks there are log-periodic oscillations of above quantities. We present real-world examples of such a behavior as well as we derive analytical expressions and compare them to numerical simulations. We consider a simple case of network optimization problem, arguing that discrete effects can lead to a nontrivial solution.
Keywords
Cite
@article{arxiv.cond-mat/0608273,
title = {Log-periodic oscillations due to discrete effects in complex networks},
author = {Julian Sienkiewicz and Piotr Fronczak and Janusz A. Holyst},
journal= {arXiv preprint arXiv:cond-mat/0608273},
year = {2007}
}
Comments
5 pages, 5 figures, REVTEX