The requirement to improve the flexibility of protection and reduce the power supply recovery time for distribution network protection control is needed. Based on dynamic topology analysis, the graphical description of the distribution network protection control system is provided to solve the problem of adaptive protection and control. Firstly, the calculation method of the correlated subgraph is studied. The adaptive dynamic adjustment of the fault identification area and fault action area of the adaptive protection control system of the distribution network is transformed into different types of correlated subgraphs. On this basis, the dynamic strategy for fault identification, action logic, and self-healing judgment for different operation and configuration are carried out. Finally, the associated subgraph algorithm and protection control decision are verified by the case, which effectively meets the self-adaptability requirements of the distribution network protection and control system. This work is supported by Science and Technology Project of China Southern Power Grid Co., Ltd. (No. SZKJXM20160056) and National Natural Science Foundation of China (No. 51577073).