We consider the verification of parameterized networks of replicated processes whose architecture is described by hyperedge-replacement graph grammars in the style of Courcelle. Due to the undecidability of verification problems such as reachability or coverability of a given configuration, in which we count the number of replicas in each local state, we develop two orthogonal verification techniques. We present a counting abstraction able to produce, from a graph grammar describing a parameterized system, a finite set of Petri nets that over-approximate the behaviors of the original system. The counting abstraction is implemented in a prototype tool, evaluated on a non-trivial set of test cases. Moreover, we identify a decidable fragment, for which the coverability problem is in 2EXPTIME and PSPACE-hard.