Stable landslide susceptibility mapping (LSM) is crucial for disaster prevention and mitigation efforts. The exploration of factor interactions and the reliability of non-landslide sampling pose challenges for deep learning-based LSM. This study developed an edge-attentive graph convolutional network (EAGCN) and built a non-landslide sample optimization framework. Our methods consist of three steps. First, graph convolution constructs a graph structure for factors, calculating edges to extract their interaction features. Second, the attention mechanism weights the coupling features by incorporating factor feature distances to optimize neighborhood feature aggregation. Third, positive-unlabeled (PU) learning scores a large number of unlabeled samples through iterative sampling and classifier learning to select reliable non-landslide samples. Our designed module can extract and utilize coupling, and factor features of arbitrary dimensions and can be embedded into any neural network layer. In southeastern Tibetan Plateau (TP), data from 798 landslides and 9 conditioning factors were prepared for usability validation and regional LSM. The evaluation results indicated that the proposed EAGCN achieved the highest the Area Under the Receiver Operating Characteristic Curve (AUC) of 98.2%, demonstrating an improvement of 3.2% to 6.4% compared with traditional machine learning (ML) methods and 2.2% compared with deep learning (DL) method. The PU non-landslide optimization sampling framework enhanced the AUC of traditional ML methods by 2.4% to 8.9% and the AUC of DL method by 4.8%. Furthermore, hyperparameter analysis of the graph structure showed that using excessively high dimensions for coupling and factor features increases model complexity, leading to decreased accuracy. Additionally, visualized feature maps demonstrated that the proposed method effectively differentiates factor feature distances and attention weights to distinguish between landslide and non-landslide samples. Finally, comparative experiments confirmed the superiority of the proposed methods in LSM.