Nowadays, social media such as microblog has developed rapidly, accelerating the spread of information on the Internet. However, many false rumors generated by social media are widely spread on social media, which may have serious consequences. Automatic detection of rumors on social media has become a major challenge in research and industry. This paper briefly introduces the detection method based on neural network graph (GNN), because it has high performance in studying the representation and relationship between nodes in the network, this paper summarizes methods for classifying neural network diagrams for rumor detection. We compare the differences and universality between different models in the information collection stage. The GNN proposal still faces problems and challenges. We hope it can provide guidance for rumor detection’s future research.