Does there exist an efficient algorithm for generating all non-isomorphic k-partite graphs up to a certain order $n$? I've read through the nauty tutorial, but it doesn't look like anything beyond bipartite graph generation is supported. Any help, whether it's a pointer to a paper(s) or source code, would be immensely useful in my research.

EDIT: One variation of my problem requires that all graphs are also regular, so I can assume a fixed degree for every node. I'm still not sure if that helps.

areproperly coloured with $t$ colours? The generation problem is entirely different for these two options. $\endgroup$ – Brendan McKay Aug 31 '13 at 0:52