The Players' Player Award which is given to the best "team player" as voted on by the players was also won by Graves in 1991–92, 1992–93, 1994–95 and 1998–99. In the 1992–93 and 1993–94 seasons, Graves won the Rangers Most Valuable Player Award given to the Rangers most valuable player as voted on by the media. Also during the 1992–93 season, Graves was given the "Rangers Good Guy" award. During the Rangers' Stanley Cup-winning season, Graves was awarded the Frank Boucher Trophy, given by the Rangers Fan Club given to the most popular player on and off the ice. Yet another fan club award Graves was awarded the "Rangers Fan Club Ceil Saidel Memorial Award" during the 1995–96, 1996–97 and 1999–2000 seasons. This award is for dedication on and off the ice.