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Three typical types of defects, i.e., keyholes, lack of fusion (LoF), and gas-entrapped pores (GEP), characterized by various features (e.g., volume, surface area, etc.), are generated under different process parameters of laser beam powder bed fusion (L-PBF) processes in additive manufacturing (AM). The different types of defects deteriorate the mechanical performance of L- PBF components, such as fatigue life, to a different extent. However, there is a lack of recognized approaches to classify the defects automatically and accurately in L-PBF components. This work presents a novel hierarchical graph convolutional network (H-GCN) to classify different types of defects by a cascading GCN structure with a low-level feature (e.g., defect features) layer and a high-level feature (e.g., process parameters) layer. Such an H-GCN not only leverages the multi- level information from process parameters and defect features to classify the defects but also explores the impact of process parameters on defect types and features. The H-GCN is evaluated through a case study with X-ray computed tomography (CT) L-PBF defect datasets and compared with several machine learning methods. H-GCN exhibits an outstanding classification performance with an F1-score of 1.000 and reveals the potential effect of process parameters on three types of defects.