Log-periodic oscillations due to discrete effects in complex networks

Sienkiewicz, Julian; Fronczak, Piotr; Holyst, Janusz A.

Log-periodic oscillations due to discrete effects in complex networks

Authors

Sienkiewicz, Julian

Fronczak, Piotr

Holyst, Janusz A.

Description

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