Coronary artery disease (CAD) stands as the leading cause of death worldwide, and invasive coronary angiography (ICA) remains the gold standard for assessing vascular anatomical information. However, deep learning-based methods encounter challenges in generating semantic labels for arterial segments, primarily due to the morphological similarity between arterial branches. To address this challenge, we model the vascular tree as a graph and propose a multi-graph graph matching (MGM) algorithm for coronary artery semantic labeling. The MGM algorithm assesses the similarity between arterials in multiple vascular tree graphs, taking into account the cycle consistency between each pair of graphs. This ensures that unannotated arterial segments are appropriately labeled by matching them with annotated segments. Through the incorporation of anatomical graph structure, radiomics features, and semantic mapping, the proposed MGM model achieves an impressive accuracy of 0.9471 for coronary artery semantic labeling. This approach presents a novel tool for coronary artery analysis using ICA videos, offering valuable insights into vascular health and pathology.