We address the problem of clustering large graph databases according to scaffolds (i.e., large structural overlaps) that are shared between cluster members. In previous work, an online algorithm was proposed for this task that produces overlapping (non-disjoint) and nonexhaustive clusterings. In this paper, we parallelize this algorithm to take advantage of high-performance parallel hardware and further improve the algorithm in three ways: a refined cluster membership test based on a set abstraction of graphs, sorting graphs according to size, to avoid cluster membership tests in the first place, and the definition of a cluster representative once the cluster scaffold is unique, to avoid cluster comparisons with all cluster members. In experiments on a large database of chemical structures, we show that running times can be reduced by a large factor for one parameter setting used in previous work. For harder parameter settings, it was possible to obtain results within reasonable time for 300,000 structures, compared to 10,000 structures in previous work. This shows that structural, scaffold-based clustering of smaller libraries for virtual screening is already feasible.