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 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

1940: Abilene Christian College Bible Lectures - Full Text

Delivered in the Auditorium of Abilene Christian College, February, 1940, Abilene, Texas. Published April, 1940 PRICE, $1.00 FIRM FOUNDATION PUBLISHING HOUSE Austin, Texas