  It has long been known that the combinatorial properties of a graph $\Gamma$
are closely related to the group theoretic properties of its right angled artin
group (raag). It's natural to ask if the graph homomorphisms are similarly
related to the group homomorphisms between two raags. The main result of this
paper shows that there is a purely algebraic way to characterize the raags
amongst groups, and the graph homomorphisms amongst the group homomorphisms. As
a corollary we present a new algorithm for recovering $\Gamma$ from its raag.
