  Cluster algebras were introduced by S. Fomin and A. Zelevinsky in connection
with dual canonical bases. To a cluster algebra of simply laced Dynkin type one
can associate the cluster category. Any cluster of the cluster algebra
corresponds to a tilting object in the cluster category. The cluster tilted
algebra is the algebra of endomorphisms of that tilting object. Viewing the
cluster tilted algebra as a path algebra of a quiver with relations, we prove
in this paper that the quiver of the cluster tilted algebra is equal to the
cluster diagram. We study also the relations. As an application of these
results, we answer several conjectures on the connection between cluster
algebras and quiver representations.
