"Winner takes it all": strongest node rule for evolution of scale free   networks
  We study a novel model for evolution of complex networks. We introduce information filtering for reduction of the number of available nodes to a randomly chosen sample, as stochastic component of evolution. New nodes are attached to the nodes that have maximal degree in the sample, which is a deterministic component of network evolution process. This fact is a novel for evolution of scale free networks and depicts a possible new route for modeling network growth. We present both simulational 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. 
H. Stefancic, V. Zlatic