  We consider the set of all graphs on n labeled vertices with prescribed
degrees D=(d_1, ..., d_n). For a wide class of tame degree sequences D we prove
a computationally efficient asymptotic formula approximating the number of
graphs within a relative error which approaches 0 as n grows. As a corollary,
we prove that the structure of a random graph with a given tame degree sequence
D is well described by a certain maximum entropy matrix computed from D. We
also establish an asymptotic formula for the number of bipartite graphs with
prescribed degrees of vertices, or, equivalently, for the number of 0-1
matrices with prescribed row and column sums.
