Graph neural networks (GNNs) are deep learning algorithms that process graph-structured data and are suitable for applications such as social networks, physical models, financial markets, and molecular predictions. Bibliometrics, a tool for tracking research evolution, identifying milestones, and assessing current research, can help identify emerging trends. This study aims to map GNN applications, research directions, and key contributors. An analysis of 40,741 GNN-related publications from the Web Science Core Collection reveals a rising trend in GNN publications, especially since 2018. Computer Science, Engineering, and Telecommunications play significant roles in GNN research, with a focus on deep learning, graph convolutional networks, neural networks, convolutional neural networks, and machine learning. China and the USA combined account for 76.4% of the publications. Chinese universities concentrate on graph convolutional networks, deep learning, feature extraction, and task analysis, whereas American universities focus on machine learning and deep learning. The study also highlights the importance of Chemistry, Physics, Mathematics, Imaging Science & Photographic Technology, and Computer Science in their respective knowledge communities. In conclusion, the bibliometric analysis provides an overview of GNN research, showing growing interest and applications across various disciplines, and highlighting the potential of GNNs in solving complex problems and the need for continued research and collaboration.