title: Kleinberg navigation in fractal small-world networks.
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 the most efficient navigation is attained when the length r of long-range links is taken from the distribution P(r) approximately r(-alpha), where alpha=d(f) is the fractal dimension of the underlying lattice. We find finite-size corrections to the exponent alpha, proportional to 1/(ln N)2.
authors.affiliation: Department of Physics, Clarkson University, Potsdam, NY 13699-5820, USA.
authors.forename: Mickey R
authors.initials: MR
authors.lastname: Roberson
authors.forename: Daniel
authors.initials: D
authors.lastname: ben-Avraham