Utilizing electromagnetic scattering information for SAR data interpretation is currently a prominent research focus in the SAR interpretation domain. Graph Neural Networks (GNNs) can effectively integrate domain-specific physical knowledge and human prior knowledge, thereby alleviating challenges such as limited sample availability and poor generalization in SAR interpretation. In this study, we thoroughly investigate the electromagnetic inverse scattering information of single-channel SAR and re-examine the limitations of applying GNNs to SAR interpretation. We propose the SAR Graph Transformer Recognition Algorithm (SAR-GTR). SAR-GTR carefully considers the attributes and characteristics of different electromagnetic scattering parameters by distinguishing the mapping methods for discrete and continuous parameters, thereby avoiding information confusion and loss. Furthermore, the GTR combines GNNs with the Transformer mechanism and introduces an edge information enhancement channel to facilitate interactive learning of node and edge features, enabling the capture of robust and global structural characteristics of targets. Additionally, the GTR constructs a hierarchical topology-aware system through global node encoding and edge position encoding, fully exploiting the hierarchical structural information of targets. Finally, the effectiveness of the algorithm is validated using the ATRNet-STAR large-scale vehicle dataset.