Rapid development in automatic vector extraction from remote sensing images has been witnessed in recent years. However, the vast majority of existing works concentrate on a specific target, fragile to category variety, and hardly achieve stable performance crossing different categories. In this work, we propose an innovative class-agnostic model, namely TopDiG, to directly extract topological directional graphs from remote sensing images and solve these issues. Firstly, TopDiG employs a topology-concentrated node detector (TCND) to detect nodes and obtain compact perception of topological components. Secondly, we propose a dynamic graph supervision (DGS) strategy to dynamically generate adjacency graph labels from unordered nodes. Finally, the directional graph (DiG) generator module is designed to construct topological directional graphs from predicted nodes. Experiments on the Inria, CrowdAI, GID, GF2 and Massachusetts datasets empirically demonstrate that TopDiG is class-agnostic and achieves competitive performance on all datasets.