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/