Convolutional neural networks (CNNs) have received widespread attention due to their powerful modeling capabilities and have been successfully applied in natural language processing, image recognition, and other fields. On the other hand, traditional CNN can only deal with Euclidean spatial data. In contrast, many real-life scenarios, such as transportation networks, social networks, reference networks, and so on, exist in graph data. The creation of graph convolution operators and graph pooling is at the heart of migrating CNN to graph data analysis and processing. With the advancement of the Internet and technology, graph convolution network (GCN), as an innovative technology in artificial intelligence (AI), has received more and more attention. GCN has been widely used in different fields such as image processing, intelligent recommender system, knowledge-based graph, and other areas due to their excellent characteristics in processing non-European spatial data. At the same time, communication networks have also embraced AI technology in recent years, and AI serves as the brain of the future network and realizes the comprehensive intelligence of the future grid. Many complex communication network problems can be abstracted as graph-based optimization problems and solved by GCN, thus overcoming the limitations of traditional methods. This survey briefly describes the definition of graph-based machine learning, introduces different types of graph networks, summarizes the application of GCN in various research fields, analyzes the research status, and gives the future research direction.