The radial constraint of distribution network is an important constraint in the optimization of distribution network, but the current methods used to judge the radiation of distribution network are more complex, which limits the efficiency of solving the related problems. In order to solve this problem, firstly, from the perspective of graph theory, the characteristics of islands and loops that may appear in the distribution network topology are analyzed, and puts forward the sufficient and necessary conditions for the distribution network to meet the radial constraint. Then, it is combined with the ring network coding method commonly used in meta heuristic algorithm, and the ring network coding method is improved. Two methods, loop method and cut set method, are proposed to detect the radial structure of distribution network and correct the infeasible solution. Finally, the proposed method is applied to the distribution network reconfiguration problem, and based on IEEE 33 bus system, the correctness and efficiency of the method is proved by comparing the calculation results and efficiency of different radiation test methods.