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Kleinberg Navigation in Fractal Small World Networks

Mickey R. Roberson·Daniel ben-Avraham
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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.

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Mickey R. Roberson, Daniel ben-Avraham. 2006-12-13. Kleinberg Navigation in Fractal Small World Networks. https://doi.org/10.1103/physreve.74.017101

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