Spectral Graph neural network has recently attracted increasing attention. Although it has been intensively research and widely applied in areas, such as link prediction, node classification, and clustering due to the powerful modeling capabilities of graph-structured data bioinformatics, 3D point cloud, Graph outlier detection, social network study, traffic networks and Hyperspectral image classification, the research of Spectral Graph Neural Network model is still in its infancy. CiteSpace was used as the tool to analyze the research hotspots and frontiers of Spectral Graph Neural Network. This study reviewed 3721 publications on Spectral Graph Neural Network between 2010 and 2023 from Web of Science Core Collection, using the appropriate keywords. CiteSpace was used to generate network maps and identify top authors, most productive country, core institutions, most high-frequency keywords, highly cited papers, and hot topics of research; and trends about co-author analysis, co-keyword analysis, co-citation analysis, and particularly cluster analysis ((Q = 0.8716)). Based on the CiteSpace outcomes, this domain is a hot topic with growing number of publications and close institutional and inter-country collaboration. Additionally, it integrates diverse disciplines and covers a wide range of topics. These results can be used by researchers and research groups’ future research directions. In addition, beyond the current utilization of graph Fourier transform and spectral graph wavelet transform, more graph data analysis methods will be introduced in the future.