In 1872, he was an assistant at the zoological institute in Strasbourg, where he worked closely with Eduard Oscar Schmidt (1823–1886).

In 1873, he relocated to Munich as an assistant to Karl Theodor Ernst von Siebold (1804–1885), gaining his habilitation during the following year.

Graff was a leading expert on Turbellaria (flatworms), especially remembered for research of its morphology and biological systematics.

He gathered material for his studies on numerous expeditions, which included journeys to Ceylon and Java (1893–94), the Arctic Ocean (1902), and North America (1907).

With Victor von Ebner (1842–1925) and others, he founded the Gesellschaft für Morphologie und Physiologie (1907).