  We study a class models of correlated random networks in which vertices are
characterized by \textit{hidden variables} controlling the establishment of
edges between pairs of vertices. We find analytical expressions for the main
topological properties of these models as a function of the distribution of
hidden variables and the probability of connecting vertices. The expressions
obtained are checked by means of numerical simulations in a particular example.
The general model is extended to describe a practical algorithm to generate
random networks with an \textit{a priori} specified correlation structure. We
also present an extension of the class, to map non-equilibrium growing networks
to networks with hidden variables that represent the time at which each vertex
was introduced in the system.
