The classification problem for measure preserving transformations is strictly more complicated than that of graph isomorphism.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm169-1-2, author = {G. Hjorth}, title = {On invariants for measure preserving transformations}, journal = {Fundamenta Mathematicae}, volume = {167}, year = {2001}, pages = {51-84}, zbl = {0990.03036}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm169-1-2} }
G. Hjorth. On invariants for measure preserving transformations. Fundamenta Mathematicae, Tome 167 (2001) pp. 51-84. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm169-1-2/