Reshuffling scale-free networks: from random to assortative.

To analyze the role of assortativity in networks we introduce an algorithm which produces assortative mixing to a desired degree. This degree is governed by one parameter p . Changing this parameter one can construct networks ranging from fully random (p=0) to totally assortative (p=1) . We apply the algorithm to a Barabási-Albert scale-free network and show that the degree of assortativity is an important parameter governing the geometrical and transport properties of networks. Thus, the average path length of the network increases dramatically with the degree of assortativity. Moreover, the concentration dependences of the size of the giant component in the node percolation problem for uncorrelated and assortative networks are strongly different. The behavior of the clustering coefficient is also discussed.