  For a countable discrete space V, every nondegenerate separable
C*-correspondence over c_0(V) is isomorphic to one coming from a directed graph
with vertex set V. In this paper we demonstrate why the analogous
characterizations fail to hold for higher-rank graphs (where one considers
product systems of C*-correspondences) and for topological graphs (where V is
locally compact Hausdorff), and we discuss the obstructions that arise.
