Kleinberg navigation in fractal small-world networks.
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.
Roberson
Mickey R
MR
Department of Physics, Clarkson University, Potsdam, NY 13699-5820, USA.
ben-Avraham
Daniel
D