Volume 63, Number 1, July 2003
|Page(s)||8 - 13|
|Published online||01 June 2003|
Small worlds, mazes and random walks
Departamento Matemática Aplicada y Estadística Escuela Superior de Ingenieros Aeronáuticos, Universidad Politécnica de Madrid Plaza Cardenal Cisneros 3, Madrid 28040, Spain
2 Departamento de Sistemas Complejos, Instituto de Física Universidad Nacional Autónoma de México, Cd Universitaria México 01000 DF, México
Accepted: 2 May 2003
A parametrized family of random walks whose trajectories are easily identified as graphs is presented. This construction shows small-world–like behavior but, interestingly, a power law emerges between the minimal distance L and the number of nodes N of the graph instead of the typical logarithmic scaling. We explain this peculiar finding in the light of the well-known scaling relationships in Random Walk Theory. Our model establishes a link between Complex Networks and Self-Avoiding Random Walks, a useful theoretical framework in polymer science.
PACS: 05.40.Fb – Random walks and Levy flights / 02.50.-r – Probability theory, stochastic processes, and statistics / 02.70.Uu – Applications of Monte Carlo methods
© EDP Sciences, 2003
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