  There are typically several nonisomorphic graphs having a given degree
sequence, and for any two degree sequence terms it is often possible to find a
realization in which the corresponding vertices are adjacent and one in which
they are not. We provide necessary and sufficient conditions for two vertices
to be adjacent (or nonadjacent) in every realization of the degree sequence.
These conditions generalize degree sequence and structural characterizations of
the threshold graphs, in which every adjacency relationship is forcibly
determined by the degree sequence. We further show that degree sequences for
which adjacency relationships are forced form an upward-closed set in the
dominance order on graphic partitions of an even integer.
