  Let Q be a quiver without loops and 2-cycles, let A(Q) be the corresponding
cluster algebra and let x be a cluster. We introduce a new class of integer
vectors which we call frieze vectors relative to x. These frieze vectors are
defined as solutions of certain Diophantine equations given by the cluster
variables in the cluster algebra. We show that every cluster gives rise to a
frieze vector and that the frieze vector determines the cluster.
  We also study friezes of type Q as homomorphisms from the cluster algebra to
an arbitrary integral domain. In particular, we show that every positive
integral frieze of affine Dynkin type A is unitary, which means it is obtained
by specializing each cluster variable in one cluster to the constant 1. This
completes the answer to the question of unitarity for all positive integral
friezes of Dynkin and affine Dynkin types.
