Background: Invasive coronary angiography (ICA) remains the gold standard for diagnosing CAD. Our objective was to develop a machine learning method for coronary semantic segmentation and stenosis detection in ICA. Method: We first extract coronary artery branches using ICAs and convert the vascular tree into ICA graphs. Then, we construct the hyper association graph from two individual ICA graphs. The vertex in the hyper association graph encodes the correspondence between two artery branches, and each hyperedge represents the correspondence between multiple artery branches. Hypergraph matching is used to find feature correspondence by considering higher-order structural information, and the artery semantic labeling task is converted into a vertex classification. Ultimately, by learning the semantic mapping of artery branches between ICAs, the unlabeled arteries are categorized by labeled arteries so that semantic segmentation is achieved. After performing the semantic labeling, a deterministic network performs stenosis detection. More specifically, a convolution long-short-term network is employed to extract imaging features, and an LSTM is employed to extract the radius features along the artery. The late fusion technology is employed to fuse the feature representation, and a softmax classifier is employed to detect the stenosis. Results: 310 ICAs from 179 subjects were collected and utilized for data analysis. Our graph-matching model achieved an average accuracy of 0.86 for coronary artery semantic labeling. The deterministic network achieved an accuracy of 0.80 for coronary artery stenosis detection. Conclusion: We have developed and validated a hypergraph-based graph-matching algorithm for coronary semantic labeling and a fusion network for artery stenosis detection. This has important implications for integrating AI software in ICA, potentially resulting in automated report generation or as an assistant for clinical decision-making.