Woods, 26, played 14 games for the Comets last season, collecting two goals and two assists.
The native of Humboldt, Sask., has appeared in 209 career AHL games with Utica and Charlotte, totaling 32 goals and 36 assists for 68 points.
A fifth-round pick by Carolina in the 2012 NHL Draft, Woods has also played seven games in the NHL with the Hurricanes.
His father, Bob, now an assistant coach with the Minnesota Wild, played 102 games with the AHL’s Utica Devils from 1989-91.
Graham, 24, notched four goals and 17 assists for 21 points in 46 games with the AHL’s San Antonio Rampage in 2017-18.
Entering his fifth professional season, Graham has registered 15 goals and 55 assists for 70 points in 163 career AHL games with San Antonio and Bridgeport.
Graham was originally selected by the New York Islanders in the sixth round of the 2012 NHL Draft.