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.
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|Publication status||Published - Mar 2 2006|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics