Recently, emerging intelligent algorithms have achieved great success in the field of sleep staging research with excellent feature extraction and learning capabilities. However, most of the current sleep staging methods focus only on the data values themselves, ignoring the relationship and topological information between the data. To address the issues mentioned above, this paper proposes a single-channel EEG sleep staging method based on horizontal visibility graph (HVG) and graph isomorphism network (GIN). Firstly, the single-channel EEG signal is converted into HVG from a geometric point of view. Then, the structure information of the graph is learned by using the latest variant GIN in the graph convolutional network (GCN), and the sleep stage is identified. The experimental results show that the sleep analysis method proposed in this paper can not only fully reflect the relationship and structural features between data, but also aggregate node information more effectively, so as to obtain more accurate graph-level representation. Therefore, this method can more accurately identify the various stages of the sleep process and improve the performance of sleep staging.