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To characterize the topological structure of a power system, we first define a dual system for the original one to handle the case where a transmission line is inoperative. Then, we introduce four new indices for a transmission line: dual power supply capacity, capacity balance ratio, dual load limit, and dual overload ratio. We use the maximum-flow algorithm of graph theory along with the indices to analyze the robustness of a power system. Unlike existing methods, this one is very simple; and there is no need to calculate the state of the system repetitively. Finally, the validity of the method is demonstrated using a power system with 18 nodes and 20 branches.