Designer nets from local strategies

Abstract

We propose a local strategy for constructing scale-free networks of arbitrary degree distributions, based on the redirection method of Krapivsky and Redner [Phys. Rev. E 63, 066123 (2001)]. Our method includes a set of external parameters that can be tuned at will to match detailed behavior at small degree k, in addition to the scale-free power-law tail signature at large k. Once achieved, the target distribution is maintained throughout the growth of the net. The method is local in that addition of a new node requires knowledge of only the immediate environs of the (randomly selected) node to which it is attached. (Global strategies require information on finite fractions of the growing net.)