  Many social networks exhibit assortative mixing so that the predictions of
uncorrelated models might be inadequate. To analyze the role of assortativity
we introduce an algorithm which changes correlations in a network and 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 Barabasi-Albert scale-free network and show that the degree of assortativity
is an important parameter governing geometrical and transport properties of
networks. Thus, the diameter of the network and the clustering coefficient
increase 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.
