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.