Kleinberg Navigation in Fractal Small World Networks

Details Kleinberg Navigation in Fractal Small World Networks Kleinberg Navigation in Fractal Small World Networks

2006-12-13

arxiv.org/abs/cond-mat/0612326v1

Phys. Rev. E 74, 017101 (2006)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevE.74.017101

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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