Single-chain nanoparticles are intriguing materials inspired by proteins that consist of a single precursor polymer chain that has collapsed into a stable structure. In many prospective applications, such as catalysis, the utility of a single-chain nanoparticle will intricately depend on the reliable formation of a mostly specific structure or morphology. However, it is not generally well understood how to reliably control the morphology of single-chain nanoparticles. To address this knowledge gap, we simulate the formation of 7,680 distinct single-chain nanoparticles from precursor chains that span a wide range of precursor sequence descriptors. Using a combination of graph-theoretic and machine learning analyses, this work shows how specific topological descriptors promotes certain local and global morphological characteristics.