I'm having trouble finding information on this because I am not familiar with the nomenclature for graph theory. If you don't know of a specific algorithm, or if you know no such algorithm exists, giving me the terms to search for in the literature would be helpful. If possible I would prefer an algorithm was at its core bayesian, using what has been seen before as a standard for what it can expect to encounter in the future. How does the answer to my question change if we have some information about the graph, like the number of nodes?
A secondary question would be to predict the labeling of nodes and edges given the nodes that have already seen. So if the graph is a simple chain, and the first node is "A" and the second node is "B" we would naturally predict the next node would be labelled "C".