Statistics of cycles in large networks

Konstantin Klemm, Peter F. Stadler

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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 t 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.

Original languageEnglish
Article number025101
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number2
Publication statusPublished - 2006

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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