Political discussions on social media have become an important source of information for understanding public opinion and information dissemination. However, most existing political topic classification methods rely primarily on textual features and tend to overlook structural and temporal relationships between users. In this study, we propose a Multi-View Graph Attention Network (MV-GAT) that improves political topic classification by integrating three complementary graph representations: a semantic content graph, a user interaction graph, and a temporal propagation graph. We collected a dataset containing 15,131 Indonesian tweets from Twitter(X), of which 1,677 tweets were manually labeled as political or apolitical, and the remaining tweets were kept as unlabeled nodes to maintain the graph structure. Each graph view was independently constructed and aligned using tweet_id before being processed by the proposed MV-GAT model. The model was trained using weighted cross-entropy loss with an attention-based fusion mechanism to automatically learn the contribution of each graph view. Experimental results showed that the proposed method achieved an accuracy of 84.23%, a macro F1 score of 83.04%, and an F1 score of 78.54% in political topic classification. Attention analysis revealed that the semantic content graph contributed most significantly to the classification process, while the interaction graph and time graph provided complementary structural information. Furthermore, post-classification graph analysis revealed relationship patterns among users and the propagation of political information within the Twitter network. These results demonstrate that integrating multiple graph views improves both the classification performance and interpretability of political topic analysis on social media.