  Recently, random graphs in which vertices are characterized by hidden
variables controlling the establishment of edges between pairs of vertices have
attracted much attention. Here, we present a specific realization of a class of
random network models in which the connection probability between two vertices
(i,j) is a specific function of degrees ki and kj. In the framework of the
configuration model of random graphs, we find analytical expressions for the
degree correlation and clustering as a function of the variance of the desired
degree distribution. The expressions obtained are checked by means of numerical
simulations. Possible applications of our model are discussed.
