2009-10: Jesse Graham skated for the Toronto Young Nationals minor midget team. In 84 games he scored 14 goals with 74 assists. Graham was selected by the Niagara IceDogs in the first round (sixth overall) of the 2010 OHL Priority Draft.
2010-11: Graham played in 63 of 68 games for Niagara in his first OHL season and was part of the gold medal-winning Canada Ontario squad at the 2011 U17 World Hockey Challenge. His plus-27 plus/minus was second only to Dougie Hamilton’s plus-35 amongst IceDogs defensemen and he scored 1 goal with 17 assists and had 22 penalty minutes. The IceDogs finished with the OHL’s third-best record and were second to Mississauga St. Michael’s in the Central Division. Niagara reached the playoff semifinals and in 14 playoff games Graham scored 1 goal with 8 assists and was plus-seven with 8 penalty minutes. In five games at the WHC he had 1 goal with 5 assists and had 2 penalty minutes.
2011-12: Graham attended Hockey Canada’s U18 summer camp before returning to Niagara for his second season with the Ice Dogs. He skated in all 68 regular season games for the IceDogs and was a big part of the team’s success; Niagara finished first in the Central Division and reached the OHL Finals against the London Knights. Graham finished plus-25 and scored 4 goals with 37 assists while accumulating 36 penalty minutes. In 20 playoff games he was minus-one and had 1 goal with 9 assists and 20 penalty minutes. Ranked 125th in Central Scouting’s final rankings prior to the 2012 NHL Draft, he was selected by the Islanders in the sixth round (155th overall).
2012-13: Graham had a big second half offensively in his third season with the OHL’s Niagara IceDogs. Over-shadowed by Dougie Hamilton during the NHL lockout, Graham had 2 goals and 19 in the IceDogs’ first 50 games. He had seven points in a five-game stretch in late January with Hamilton in Boston and had eight points in seven games in March; finishing the year with 4 goals and 35 assists in 68 games. Graham was minus-17 with 48 penalty minutes on a Niagara team missing several scorers from the team that reached the OHL Finals. The IceDogs slipped to fourth in the Central Division and lost to Oshawa in the first round. Graham had 3 assists in five playoff games and was an even plus/minus with 6 penalty minutes.
2013-14: Graham attended NHL training camp with the Islanders before being sent back to juniors for his fourth OHL season; making his pro hockey debut with New York AHL affiliate Bridgeport following his junior season. In seven games with the Sound Tigers he scored 1 goal, a power play goal, with 3 assists and had an even plus/minus with 2 penalty minutes. Bridgeport finished fifth in the Northeast Division, missing the AHL playoffs. Graham began the season with Niagara, skating in 24 games as the IceDogs’ team captain before being acquired by Saginaw in an OHL trade in November. In 66 regular season games between the two teams he scored 11 goals with 43 assists, both career highs, and was plus-3 with 43 penalty minutes. Saginaw finished third in the West Division and lost to Erie in a first round playoff series. Graham had 3 assists and was plus-1 with 2 penalty minutes in five playoff games. He signed a three-year entry-level contract with the Islanders in May 2014.
2014-15: Graham split his first pro season between the AHL and ECHL — skating in 39 games for Islanders’ AHL affiliate Bridgeport as a 20-year-old. He scored 3 goals with 15 assists and was -5 with 20 penalty minutes with the Sound Tigers. Bridgeport missed the AHL playoffs, finishing last in the Northeast Division. Graham played 23 regular season ECHL games with the Florida Everblades. He scored 1 goal with 13 assists and was +7 with 10 penalty minutes. Florida finished first in the East Division and reached the second round in the Kelly Cup playoffs. Graham led Everblades defensemen with six points in 12 playoff games — scoring 1 goal with 5 assists — and was +1 with 4 penalty minutes.
Graham is an offensively-inclinded defenseman whose speed gives him an advantage on the opposition — both in his defensive zone and in the transition. He can create space with his feet and open up lanes in transition. Part of a crowded group of defense prospects, he spent time at the ECHL level in his first pro season but took advantage of the opportunity to play in all situations; leading the Florida Everblades defensemen in scoring in the Kelly Cup playoffs.
Graham is in his second pro season in 2015-16. He has been an offensive threat from the back end during his time with the AHL's Bridgeport Sound Tigers and with the depth in the Islanders' system has also skated for the ECHL's Missouri Mavericks. Graham faces stiff competition but his play to this point suggests he can be a quality two-way defender at the NHL level.