  In this paper we prove that Graded Calabi Yau Algebras of dimension 3 are
isomorphic to path algebras of quivers with relations derived from a
superpotential. We show that for a given quiver $Q$ and a degree $d$, the set
of good superpotentials of degree $d$, i.e. those that give rise to Calabi Yau
algebras is either empty or almost everything (in the measure theoretic sense).
We also give some constraints on the structure of quivers that allow good
superpotentials, and for the simplest quivers we give a complete list of the
degrees for which good superpotentials exist.
