  (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.
