Graves, a native of Yarmouth, Nova Scotia, first played at the major midget level with the South Shore Mustangs of the Nova Scotia Major Midget Hockey League as well as his local side, the Yarmouth Mariners in the Maritime Junior A Hockey League in the 2010–11 season. With his growing frame, Graves was initially selected in the first round, 9th overall, in the 2011 QMJHL Entry Draft by the Prince Edward Island Rocket. Agreeing to terms with the Rocket, Graves made his debut in the Quebec Major Junior Hockey League in the following 2011–12 season, registering 2 goals and 9 points in 62 contests. After improving his offensive output in the following 2012–13 season, Graves gained the eye of NHL scouts, and was later selected in the fourth round, 110th overall, by the New York Rangers in the 2013 NHL Entry Draft. The Rocket were rebranded as the Charlottetown Islanders for the 2013–14 season. In collecting 12 points in 39 games, Graves was dealt by the Islanders to the Val-d'Or Foreurs for their post-season push. He helped the Foreurs in the playoffs with 8 points in 24 games to help the club claim the President's Cup. On March 17, 2014, Graves' progression was rewarded as he was signed to a three-year, entry-level contract with the Rangers. Prior to the 2014–15 season, Graves was again on the move in the QMJHL, traded by the Foreurs to the Quebec Remparts in exchange for Vincent Lanoue and draft picks on August 18, 2014. An assistant captain, Graves broke out offensively in his final junior season, contributing with a career-high 15 goals and 24 assists for 39 points in just 50 games. He was selected to the Canadian Hockey League'sMemorial Cup All-Star Team after collecting 5 points in 5 games for host club Quebec.
Professional
In the 2015–16 season, Graves was assigned to the Rangers AHL affiliate, the Hartford Wolf Pack. He made his professional debut on opening night against the St. John's IceCaps on October 10, 2015. He collected his first goal and assist in a 4–3 victory over the Syracuse Crunch on October 23, 2015. As a hulking defenceman with good mobility, Graves was a staple on the blueline for the Wolf Pack and represented the club at the 2016 AHL All-Star Game, winning the hardest shot contest with a 103.4 m/ph slapshot. With the Wolf Pack finishing out of playoff contention, Graves finished the season, leading the blueline with 9 goals in his 21 points in 74 games. In the following 2016–17 season, Graves continued his upward development in leading the blueline in all scoring categories with 8 goals, 22 assists and 30 points. Assigned to the Wolf Pack for the final year of his rookie contract, Graves regressed with just 4 goals and 11 points in 57 games in the 2017–18 season. Graves was dealt by the New York Rangers at the trade deadline to the Colorado Avalanche in exchange for Chris Bigras on February 26, 2018. He was immediately assigned to the Avalanche's AHL affiliate, the San Antonio Rampage. Graves scored his first NHL goal on January 4, 2019 against the team that drafted him, the New York Rangers.
