Lynchburg Hillcats
Graham pitched for the Lynchburg Hillcats of the Class A-Advanced Carolina League and the Mississippi Braves of the Class AA Southern League in 2012 and 2013. He went 12–2 with a 2.80 earned run average and 110 strikeouts in 148 innings pitched. Prior to the 2013 season, "Baseball America" ranked Graham as the 93rd best prospect in baseball.