In the domain of analog circuit design, the retrieval of circuit diagrams has drawn a great interest, primarily due to its vital role in the consultation of legacy designs and the detection of design plagiarism. Existing image retrieval techniques are adept at handling natural images, which converts images into feature vectors and retrieval similar images according to the closeness of these vectors. Nonetheless, these approaches exhibit limitations when applied to the more specialized and intricate domain of circuit diagrams. This paper presents a novel approach to circuit diagram retrieval by employing a graph representation of circuit diagrams, effectively reformulating the retrieval task as a graph retrieval problem. The proposed methodology consists of two principal components: a circuit diagram recognition algorithm designed to extract the circuit components and topological structure of the circuit using proposed GAM-YOLO model and a 2-step connected domain filtering algorithm, and a hierarchical retrieval strategy based on graph similarity and different graph representation methods for analog circuits. Our methodology pioneers the utilization of graph representation in the retrieval of circuit diagrams, incorporating topological features that are commonly overlooked by standard image retrieval methods. The results of our experiments substantiate the efficacy of our approach in retrieving circuit diagrams across of different types.