Kleinberg Navigation in Fractal Small World Networks
Statistical Mechanics
2007-05-23 v1
Abstract
We study the Kleinberg problem of navigation in Small World networks when the underlying lattice is a fractal consisting of N>>1 nodes. Our extensive numerical simulations confirm the prediction that most efficient navigation is attained when the length r of long-range links is taken from the distribution P(r)~r^{-alpha}, where alpha=d_f, the fractal dimension of the underlying lattice. We find finite-size corrections to the exponent alpha, proportional to 1/(ln N)^2.
Keywords
Cite
@article{arxiv.cond-mat/0612326,
title = {Kleinberg Navigation in Fractal Small World Networks},
author = {Mickey R. Roberson and Daniel ben-Avraham},
journal= {arXiv preprint arXiv:cond-mat/0612326},
year = {2007}
}