Hamiltonian diversity: effectively measuring molecular diversity by shortest Hamiltonian circuits

In recent years, significant advancements have been made in molecular generation algorithms aimed at facilitating drug development, and molecular diversity holds paramount importance within the realm of molecular generation. Nonetheless, the effective quantification of molecular diversity remains an elusive challenge, as extant metrics exemplified by Richness and Internal Diversity fall short in concurrently encapsulating the two main aspects of such diversity: quantity and dissimilarity. To address this quandary, we propose Hamiltonian diversity, a novel molecular diversity metric predicated upon the shortest Hamiltonian circuit. This metric embodies both aspects of molecular diversity in principle, and we implement its calculation with high efficiency and accuracy. Furthermore, through empirical experiments we demonstrate the high consistency of Hamiltonian diversity with real-world chemical diversity, and substantiate its effects in promoting diversity of molecular generation algorithms. Our implementation of Hamiltonian diversity in Python is available at: https://github.com/HXYfighter/HamDiv .Scientific contributionWe propose a more rational molecular diversity metric for the community of cheminformatics and drug development. This metric can be applied to evaluation of existing molecular generation methods and enhancing drug design algorithms.