How to construct a correlated net
  (a) We propose a ``static'' construction procedure for random networks with given correlations of the degrees of the nearest-neighbor vertices. This is an equilibrium graph, maximally random under the constraint that its degree-degree distribution is fixed. (b) We generalize the notion of preferential linking and introduce a new category, {\em pair preference} and a pair preference function for the attaching of edges to pairs of vertices. This allows dynamically generate equilibrium correlated networks. 
S.N. Dorogovtsev, J.F.F. Mendes, A.N. Samukhin