For eight seasons, he was Music Director of the Calgary Philharmonic Orchestra. He has also served as the conductor of the Orchestre National Bordeaux Aquitaine, France for six seasons. He has been Music Director of the Houston Symphony since 2001, having debuted with them in 2000. In September 2004, Graf made his first contract extension with the Houston Symphony, through the 2008-2009 season. He made his Carnegie Hall conducting debut with the Houston Symphony in January 2006 In July 2007, Graf further extended his contract with the Houston Symphony through the 2011-2012 season. His recordings include works by Wolfgang Amadeus Mozart, Henri Dutilleux, Bela Bartók, Igor Stravinsky, and the opera Es war einmal of Alexander von Zemlinsky.
In private life, Graf is known as a wine connoisseur. He and his wife Margarita have a daughter, Anna.