“Winner takes it all”: Strongest node rule for evolution of scale-free networks

Abstract

We study a model for evolution of complex networks. We introduce information filtering for reduction of the number of available nodes to a randomly chosen sample, as a stochastic component of evolution. New nodes are attached to the nodes that have maximal degree in the sample. This is a deterministic component of network evolution process. This fact is unusual for evolution of scale-free networks and depicts a possible route for modeling network growth. We present both simulations and theoretical results for network evolution. The obtained degree distributions exhibit an obvious power-law behavior in the middle with the exponential cut off in the end. This highlights the essential characteristics of information filtering in the network growth mechanisms.