title: Statistics of cycles in large networks.
abstract: The occurrence of self-avoiding closed paths (cycles) in networks is studied under varying rules of wiring. As a main result, we find that the dependence between network size and typical cycle length is algebraic, (h) proportional to Nalpha, with distinct values of for different wiring rules. The Barabasi-Albert model has alpha=1. Different preferential and nonpreferential attachment rules and the growing Internet graph yield alpha<1. Computation of the statistics of cycles at arbitrary length is made possible by the introduction of an efficient sampling algorithm.
authors.affiliation: Department of Bioinformatics, University of Leipzig, Härtelstrasse 16-18, D-04107 Leipzig, Germany.
authors.forename: Konstantin
authors.initials: K
authors.lastname: Klemm
authors.forename: Peter F
authors.initials: PF
authors.lastname: Stadler