Graf began his collegiate career for the Union College during the 2021–22 season, where he recorded 11 goals and 11 assists in 37 games.

[2] During the 2022–23 season, in his sophomore year, he recorded a team-high 20 goals and 38 assists in 40 games.

Following the season, he was again named a unanimous All-ECAC First Team selection and ECAC Hockey Player of the Year.

[14] On April 4, 2024, Graf signed a three-year, entry-level contract with the San Jose Sharks of the National Hockey League.

[17] Graf got his first point in his second game, on April 7, assisting on a goal by Luke Kunin in a 5–2 loss to the Arizona Coyotes.