Machine learning, particularly graph learning, is gaining increasing recognition for its transformative impact across various fields. One such promising application is in the realm of molecule design and discovery, notably within the pharmaceutical industry. Our survey offers a comprehensive overview of state-of-the-art methods in molecule design, particularly focusing on \emph{de novo} drug design, which incorporates (deep) graph learning techniques. We categorize these methods into three distinct groups: \emph{i)} \emph{all-at-once}, \emph{ii)} \emph{fragment-based}, and \emph{iii)} \emph{node-by-node}. Additionally, we introduce some key public datasets and outline the commonly used evaluation metrics for both the generation and optimization of molecules. In the end, we discuss the existing challenges in this field and suggest potential directions for future research.
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