While working on some other problem I realized I need to generate (not only enumerate!) all unlabeled graph (or exactly ONE representative from each equivalence class of labeled graphs) with a certain number of vertices or edges (vertices would be enough as I can group them by edges later).
Generating all labeled graphs and then choosing a representative from each class is NOT an option. This would take too long.
Something like "the orderly method" from this website http://www.cs.uc.edu/~andersr9/interests/enumeration-of-unlabeled-graphs/ would work for me, but I couldn't find the original source.
Remark: A description of a canonical way of labeling an unlabeled graph will probably be enough for me at this moment. I might be able to devise an algorithm from there. However, a more precise answer would be greatly appreciated.