  We demonstrate a practical and efficient method for generating toric
Calabi-Yau quiver theories, applicable to both D3 and M2 brane world-volume
physics. A new analytic method is presented at low order parametres and an
algorithm for the general case is developed which has polynomial complexity in
the number of edges in the quiver. Using this algorithm, carefully implemented,
we classify the quiver diagram and assign possible superpotentials for various
small values of the number of edges and nodes. We examine some preliminary
statistics on this space of toric quiver theories.
