With the rapid development of more-electric and all-electric aircraft, the role of power supply systems in aircraft is becoming increasingly prominent. However, due to the complex coupling within the power supply system, a fault in one component often leads to parameter abnormalities in multiple components within the system, which are termed associated faults. Compared with conventional faults, the diagnosis of associated faults is difficult because the fault source is hard to trace and the fault mode is difficult to identify accurately. To this end, this paper proposes a graph-matching approach for the associated fault diagnosis of power supply systems based on a deep residual shrinkage network. The core of the proposed approach involves supplementing the incomplete prior fault knowledge with monitoring data to obtain a complete cluster of associated fault graphs. The association graph model of the power supply system is first constructed based on a topology with characteristic signal propagation and the associated measurements of typical components. Furthermore, fault propagation paths are backtracked based on the Warshall algorithm, and abnormal components are set to update and enhance the association relationship, establishing a complete cluster of typical associated fault mode graphs and realizing the organic combination and structured storage of knowledge and data. Finally, a deep residual shrinkage network is used to diagnose the associated faults via graph matching between the current state graph and the historical graph cluster. The comparative experiments conducted on the simulation model of an aircraft power supply system demonstrate that the proposed method can achieve high-precision associated fault diagnosis, even under circumstances where there are an insufficient number of samples and missing parameters.