Graham was selected 89th overall by the
Vancouver Canucks in the
1979 NHL entry draft after spending four years with the
Regina Pats in the
Western Hockey League. Graham spent four years in the minor leagues which included the
International Hockey League and the
Central Hockey League. In 1980–81, Graham scored 40 goals with the
Toledo Goaldiggers of the IHL, and he was named to the second all-star team. In 1982–83, he scored 70 goals with the Goaldiggers and was named to the first all-star team. This caught the attention of some, and he was signed as a free agent by the
Minnesota North Stars after never playing a game with the Canucks. Graham spent two more years developing in the
American Hockey League and Central Hockey League. He was selected to the CHL First All-Star Team in 1983–84. In
1985–86, Graham was playing full-time with the North Stars. He recorded consecutive 20 goal seasons in Minnesota and was chosen to represent
Team Canada in the
1987 World Ice Hockey Championships. On January 2,
1988, Graham was traded to the
Chicago Blackhawks for
Curt Fraser. Graham played his best hockey in Chicago. In his first full season with the Blackhawks (1988–89), Graham topped the 30 goal mark for the first time in his career and finished with a career high 78 points (A stunning 10 of his 33 goals were short-handed; thus he joins
Wayne Gretzky,
Mario Lemieux, and
Marcel Dionne as one of only four players to achieve ten or more short-handed goals in a season). He scored 20 goals or more four times with the Blackhawks. In
1990–91, he won the
Frank J. Selke Trophy for best defensive forward in the league and represented Team Canada in the
Canada Cup tournament. Canada would beat the
United States to take first place. Late in
1988–89, Graham was named team
captain (replacing
Denis Savard), the first player of African descent to become team captain in the
National Hockey League. He captained the team all the way to the
Stanley Cup Final in
1991–92, where they were swept by the
Pittsburgh Penguins. Graham retired in
1995 after the lockout shortened season. ==Post-playing career==