Kleinberg Navigation in Fractal Small World Networks
Mickey R. Roberson, Daniel ben-Avraham
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=df, the fractal dimension of the underlying lattice. We find finite-size corrections to the exponent alpha, proportional to 1/(ln N)2.
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