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Log-periodic oscillations due to discrete effects in complex networks

Julian Sienkiewicz·Piotr Fronczak·Janusz A. Holyst
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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 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.

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Julian Sienkiewicz, Piotr Fronczak, Janusz A. Holyst. 2006-08-11. Log-periodic oscillations due to discrete effects in complex networks. https://doi.org/10.1103/physreve.75.066102

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