Communication networks are important infrastructures in contemporary society. There are still many challenges that are not fully solved and new solutions are proposed continuously in this active research area. In recent years, to model the network topology, graph-based deep learning has achieved state-of-the-art performance in a series of problems in communication networks. In this survey, we review the rapidly growing body of research using different graph-based deep learning models, e.g. graph convolutional and graph attention networks, in various problems from different communication networks, e.g. wireless networks, wired networks, and software-defined networks. We also present a well-organized list of the problem and solution for each study and identify future research directions. To the best of our knowledge, this paper is the first survey that focuses on the application of graph-based deep learning methods in communication networks. To track the follow-up research, a public GitHub repository is created, where the relevant papers will be updated continuously.