  Let d = (d1, d2, ..., dn) be a vector of non-negative integers with even sum.
We prove some basic facts about the structure of a random graph with degree
sequence d, including the probability of a given subgraph or induced subgraph.
Although there are many results of this kind, they are restricted to the sparse
case with only a few exceptions. Our focus is instead on the case where the
average degree is approximately a constant fraction of n. Our approach is the
multidimensional saddle-point method. This extends the enumerative work of
McKay and Wormald (1990) and is analogous to the theory developed for bipartite
graphs by Greenhill and McKay (arXiv:math/0701600, 2009).
