Small worlds, mazes and random walks
Abstract
A parametrized family of random walks whose trajectories are easily identified as graphs is presented. This construction shows smallworld 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 wellknown scaling relationships in Random Walk Theory. Our model establishes a link between Complex Networks and SelfAvoiding Random Walks, a useful theoretical framework in polymer science.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 July 2003
 DOI:
 10.1209/epl/i2003004704
 arXiv:
 arXiv:condmat/0211383
 Bibcode:
 2003EL.....63....8L
 Keywords:

 05.40.Fb;
 02.50.r;
 02.70.Uu;
 Random walks and Levy flights;
 Probability theory stochastic processes and statistics;
 Applications of Monte Carlo methods;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics
 EPrint:
 article, 7 figures