2010-11: Ryan Graves played four Junior A games with the Yarmouth Mariners and skated for the Canadien Tire Mustangs midget team in Bridgewater, Nova Scotia. He had no points and 4 penalty minutes in four games with Yarmouth, including three playoff games. Graves scored 5 goals with 7 assists and had 58 penalty minutes in 32 regular season games for the Mustangs and had 6 assists with 8 penalty minutes in five playoff games. He represented Team Nova Scotia in the 2011 Canada Winter Games and had 1 assist and 4 penalty minutes in seven games. Graves was selected by Prince Edward Island in the first round (ninth overall) of the 2011 QMJHL Entry Draft.
2011-12: Graves appeared in 62 games for Prince Edward Island in his first QMJHL season and represented Canada Atlantic in the 2012 U17 World Hockey Challenge. He scored 2 goals with 7 assists and was -23 with 34 penalty minutes for the Rocket. PEI missed the playoffs after finishing last in the Maritimes Division. Graves had no points and 2 penalty minutes in five games for Canada Atlantic at the WHC.
2012-13: Graves was one of three player to skate in all 68 games as the Rocket were one of the QMJHL's big turnaround stories. He scored 3 goals with 13 assists and was +7 with 90 minutes. PEI finished third in the Maritimes Division, winning 41 games. Graves was -2 with no points and 6 penalty minutes in the six-game playoff series with Val d'Or. Ranked 116th amongst North American skaters in Central Scouting's final rankings, he was selected by the Rangers in the fourth round (110th overall) of the 2013 NHL Draft.