Eur. Phys. J. B 66, 251-257 (2008)
https://doi.org/10.1140/epjb/e2008-00401-9

Loop statistics in complex networks

Department of Physics, University of Seoul, Seoul, 130-743, Korea

Corresponding author: ^a jdnoh@uos.ac.kr

Received: 29 April 2008
Revised: 8 August 2008
Published online: 30 October 2008

Abstract

We study a scaling property of the number M_h(N) of loops of size h in complex networks with respect to a network size N. For networks with a bounded second moment of degree, we find two distinct scaling behaviors: M_h(N) ~ (constant) and M_h(N) ~ lnN as N increases. Uncorrelated random networks specified only with a degree distribution and Markovian networks specified only with a nearest neighbor degree-degree correlation display the former scaling behavior, while growing network models display the latter. The difference is attributed to structural correlation that cannot be captured by a short-range degree-degree correlation.