In response to the problem of topological identification for multi-ring power distribution networks and considering the possibility of partial loss of measurement information, a method for topological identification of multi-ring power distribution networks based on deep neural networks and Euclidean distance is proposed. First, the limitations of the traditional topological identification method using correlation judgment in ring-shaped power distribution networks are analyzed. Based on this, a topological identification criterion based on Euclidean distance is proposed. Then, to address the issue of topological identification of multi-ring networks with missing measurement information, a method combing deep neural networks with the Euclidean distance criteria is proposed. Finally, a 32-node “honeycomb” power grid model is built in Matlab using MatPower, and the accuracy of the method is verified under different levels of missing measurement data. The results show that even with a large amount of missing measurement data, the proposed method still maintains a high accuracy for topological identification.