We demonstrate how to generalize two of the most well-known random graph models, the  classic random graph, and  random graphs with a given degree distribution, by the introduction of hidden variables in the form of extra degrees of freedom, color, applied to vertices or stubs (half-edges). The color is assumed unobservable, but is allowed to affect edge probabilities. This serves as a convenient method to define very general classes of models within a common unifying formalism, and allows for a non-trivial edge correlation structure.

PACS numbers: 02.50.--r, 64.60.--i, 89.75.Fb