Graham was born in Apex, North Carolina, the second of nine children born to Alexander (September 12, 1844-November 2, 1934) and Katherine B. Sloan (March 8, 1855-January 1, 1939) Graham. He played college ball at the University of North Carolina at Chapel Hill and in the minor leagues for three years before joining the Giants on May 23, 1905. On June 29, the Giants were the visiting team against the Brooklyn Superbas. For the bottom of the eighth inning, Graham was sent in to play right field, replacing George Browne. In the top of the ninth inning, Graham was on deck (scheduled to be the next batter) when his teammate Claude Elliott flied out resulting in the third and final out. Graham played the bottom of the ninth in right field but never came to bat, and that game turned out to be his only appearance in the major leagues.
After playing in the minor leagues through the season, Graham completed his medical degree from the University of Maryland in 1908. He obtained his license the following year and began practicing medicine in Chisholm, Minnesota.
"Doc" Graham, as he became known after his career as a ballplayer, served the people of Chisholm for fifty years. From 1915 to 1959, Graham was the doctor for the Chisholm schools. The Graham Scholarship Fund, established in his honor, provides financial assistance to two Chisholm High School graduating seniors each year. The award is given to one boy and one girl, $500 to each.
Graham died at age 87 in Chisholm in 1965. He is buried in Rochester, Minnesota.
In the novel, the dates of Graham's big-league appearance and death are kept as in real life, making the 1905 appearance 74 years prior to the book's 1979 timeframe, and the Ray Kinsella character quickly finds out that Graham has been dead since 1965. The time-travel scene has Kinsella meeting Graham in 1955, ten years prior to Graham's death.
In the movie, the Fenway Park scoreboard shows Graham's appearance as having taken place in 1922, 66 years prior to the film's 1988. A woman in Minnesota familiar with Graham later says Graham had passed away in 1972. In the time-travel sequence of the movie, lead character Ray Kinsella goes back to the year of Graham's death, and is told that his appearance was at the end of the season, rather than the middle.