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 contribution We 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.

中文翻译：

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哈密​​顿多样性：通过最短哈密顿电路有效测量分子多样性


近年来，旨在促进药物开发的分子生成算法取得了重大进展，分子多样性在分子生成领域至关重要。尽管如此，分子多样性的有效量化仍然是一个难以捉摸的挑战，因为以丰富度和内部多样性为代表的现有指标无法同时概括这种多样性的两个主要方面：数量和相异性。为了解决这个难题，我们提出了哈密顿多样性，这是一种基于最短哈密顿回路的新型分子多样性度量。该指标原则上体现了分子多样性的两个方面，我们以高效、准确的方式实现了其计算。此外，通过实证实验，我们证明了哈密顿多样性与现实世界化学多样性的高度一致性，并证实了其在促进分子生成算法多样性方面的作用。我们在 Python 中实现的哈密顿多样性可以在以下位置找到：https://github.com/HXYfighter/HamDiv。科学贡献我们为化学信息学和药物开发界提出了一种更合理的分子多样性指标。该指标可应用于评估现有的分子生成方法和增强药物设计算法。