Graph embeddings are mentioned below, but also explore graph convolutional neural networks and message-passing neural networks. These methods are extensions of traditional CNN's into graph structures - after all, isn't an image just a lattice graph with pixels as nodes? These models can be used for, as also mentioned below, node and edge prediction/completion, but they can also be used for entire graph-based prediction. I've worked on graph-based prediction for molecular modeling, where I do whole-graph classification.