Anomaly analytics is a popular and vital task in various research contexts that has been studied for several decades. At the same time, deep learning has shown its capacity in solving many graph-based tasks, like node classification, link prediction, and graph classification. Recently, many studies are extending graph learning models for solving anomaly analytics problems, resulting in beneficial advances in graph-based anomaly analytics techniques. In this survey, we provide a comprehensive overview of graph learning methods for anomaly analytics tasks. We classify them into four categories based on their model architectures, namely graph convolutional network, graph attention network, graph autoencoder, and other graph learning models. The differences between these methods are also compared in a systematic manner. Furthermore, we outline several graph-based anomaly analytics applications across various domains in the real world. Finally, we discuss five potential future research directions in this rapidly growing field.