Abstract: The rapid development of energy internet has put forward new requirements for the shape, structure and function of the power grid. Aiming at the construction of the target grid structure of the distribution network, a method of evaluating the reliability of the distribution network based on graph theory is proposed. The structure is represented by the adjacency matrix of the graph, and the edge weights of the weighted adjacency matrix are used to represent the reliability parameters of the components in the feeder of the distribution network. The search tree method is used to find the minimum path of the distribution network with complex structure, which is transformed into the minimum cut set matrix to obtain the first and second order cut sets of the network. Secondly, the state-space method of graph theory is used to derive the equivalent combined calculation formula of multi-component system reliability index. For complex structure distribution networks with branch feeders, the network equivalent method is used to reflect the influence of the branch feeder on the upper feeder with the reliability index of the equivalent component. Network equivalents can effectively reduce the space complexity of the switching network frame, simplify the calculation process, and have good practical application value. Finally, the validity of applying graph theory and network equivalents to the reliability evaluation of distribution network is verified on the main feeder of RBTS bus 6 system.