  In contrast with knots, whose properties depend only on their extrinsic
topology in $S^3$, there is a rich interplay between the intrinsic structure of
a graph and the extrinsic topology of all embeddings of the graph in $S^3$ .
For example, it was shown in [2] that every embedding of the complete graph
$K_7$ in $S^3$ contains a non-trivial knot. Later in it was shown that for
every $m \in N$, there is a complete graph $K_n$ such that every embedding of
$K_n$ in $S_3$ contains a knot $Q$ whose minimal crossing number is at least
$m$. Thus there are arbitrarily complicated knots in every embedding of a
sufficiently large complete graph in $S^3$. We prove here the contrasting
result that every graph has an embedding in $S^3$ such that every non-trivial
knot in that embedding is hyperbolic. Our theorem implies that every graph has
an embedding in $S^3$ which contains no composite or satellite knots.
