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.