The computational demands of neural architecture search (NAS) algorithms are usually directly proportional to the size of their target search spaces. Thus, limiting the search to high-quality subsets can greatly reduce the computational load of NAS algorithms. In this paper, we present Clustering-Based REDuction (C-BRED), a new technique to reduce the size of NAS search spaces. C-BRED reduces a NAS space by clustering the computational graphs associated with its architectures and selecting the most promising cluster using proxy statistics correlated with network accuracy. When considering the NAS-Bench-201 (NB201) data set and the CIFAR-100 task, C-BRED selects a subset with 70% average accuracy instead of the whole space’s 64% average accuracy.