The scales of the power distribution networks in real-world power grids expand quickly while the network structures are becoming more and more complex. The power grid companies analyze the power distribution networks in different business scenarios with different topology models. In this work, we propose a hierarchical graph model to describe the medium-voltage distribution network (which is a typical power distribution network in power grids) based on homeomorphic transformation. The hierarchical graph model preserves the basic network topology described by the traditional Common Information Model (CIM). Firstly, the nodes in the distribution network topology are classified according to graph theory. Secondly, three typical business scenarios of distribution network topology analysis are summarized, and the original model is simplified by progressive dimensionality reduction method to meet the analysis requirements of different scenarios, the simplified method consists of three abstract levels: critical path, core path and minimal path, and can effectively reduce the space complexity of the model while maintaining the topological properties. Thirdly, a multi-level distribution network topology construction and mapping method based on the graph database is proposed. It is used to realize the rapid conversion and traceability between different levels of topology. Finally, a practical distribution network in a county is used as an example to verify the effectiveness of the proposed method in the aspects such as topology rendering and path searching. The evaluation indicates that the proposed model can visualize the distribution network intuitively. The model can also speed up the visualization and path searching significantly.