Log-periodic oscillations due to discrete effects in complex networks
arXiv:cond-mat/0608273 · doi:10.1103/PhysRevE.75.066102
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.
5 pages, 5 figures, REVTEX
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