Loop statistics in complex networks
Department of Physics, University of Seoul, Seoul, 130-743, Korea
Corresponding author: a firstname.lastname@example.org
Revised: 8 August 2008
Published online: 30 October 2008
We study a scaling property of the number Mh(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: Mh(N) ~ (constant) and Mh(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.
PACS: 89.75.Hc – Networks and genealogical trees / 05.10.-a – Computational methods in statistical physics and nonlinear dynamics / 05.50.+q – Lattice theory and statistics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2008