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We study the Kleinberg problem of navigation in small-world networks when the underlying lattice is a fractal consisting of N1 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)~r^-α, where α=df is the fractal dimension of the underlying lattice. We find finite-size corrections to the exponent α, proportional to 1∕(ln0.2em0exN)².
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Roberson et al. (2006) studied this question.
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