%0 Journal Article %1 Klemm2006 %A Klemm, Konstantin %A Stadler, Peter F. %D 2006 %I American Physical Society %J Physical Review E %K cycles graphs loops networks %N 2 %P 025101 %R 10.1103/PhysRevE.73.025101 %T Statistics of cycles in large networks %V 73 %X 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 N and typical cycle length is algebraic, ⟨h⟩∝Nα, with distinct values of α for different wiring rules. The Barabasi-Albert model has α=1. Different preferential and nonpreferential attachment rules and the growing Internet graph yield α<1. Computation of the statistics of cycles at arbitrary length is made possible by the introduction of an efficient sampling algorithm.

@article{Klemm2006, 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 N and typical cycle length is algebraic, ⟨{h⟩∝Nα}, with distinct values of α for different wiring rules. The {Barabasi-Albert} model has α=1. Different preferential and nonpreferential attachment rules and the growing Internet graph yield α<1. Computation of the statistics of cycles at arbitrary length is made possible by the introduction of an efficient sampling algorithm.}, added-at = {2011-03-22T17:06:20.000+0100}, author = {Klemm, Konstantin and Stadler, Peter F.}, biburl = {https://www.bibsonomy.org/bibtex/26ba4ded003fe26d74d3e6a9613dafdf2/rincedd}, doi = {10.1103/PhysRevE.73.025101}, interhash = {37401642a6be43c59297d9575248871b}, intrahash = {6ba4ded003fe26d74d3e6a9613dafdf2}, journal = {Physical Review E}, keywords = {cycles graphs loops networks}, number = 2, pages = 025101, publisher = {American Physical Society}, timestamp = {2011-03-22T17:06:20.000+0100}, title = {Statistics of cycles in large networks}, volume = 73, year = 2006 }