Log-periodic oscillations due to discrete effects in complex networks.
We show how discretization affects two major characteristics in complex networks: internode distances (measured as the shortest number of edges between network sites) and average path length, and as a result there are log-periodic oscillations of the above quantities. The effect occurs both in numerical network models as well as in such real systems as coauthorship, language, food, and public transport networks. Analytical description of these oscillations fits well numerical simulations. We consider a simple case of the network optimization problem, arguing that discrete effects can lead to a nontrivial solution.
Sienkiewicz
Julian
J
Center of Excellence for Complex Systems Research, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland.
Fronczak
Piotr
P
Hołyst
Janusz A
JA