  We construct a graph G such that any embedding of G into R^{3} contains a
nonsplit link of two components, where at least one of the components is a
nontrivial knot. Further, for any m < n we produce a graph H so that every
embedding of H contains a nonsplit n component link, where at least m of the
components are nontrivial knots.
  We then turn our attention to complete graphs and show that for any given n,
every embedding of a large enough complete graph contains a two component link
whose linking number is a nonzero multiple of n.
