Graham graduated from Junction High School and attended the University of Texas at Austin for a short time.
His father, then Kimble County Sheriff, didn't think too highly of his son's hobby, remarking that he should spend more time on the ground, tending to business.
He later flew across the Atlantic Ocean and Africa to a duty station in India, leaving his wife at home, pregnant with their first child.
He flew The Hump across the Himalayan mountains between India and Burma, delivering planes, troops and cargo in support of the effort to defeat the Japanese.
Graham discovered a number of irregularities; however, not enough proof was gained in the short time required to contest the primary results, and LBJ went on to win the seat in the general election.
Another legislative action taken by Graham that directly affected the people of Kimble County was preventing the closure of the Kerrville State Hospital, a facility that has served not only this community, but many others as well.
Following his two terms in the Texas House, Callan and Maude moved their family to San Antonio, where he took a position with a law firm.
In 1954, he accepted the position of general counsel for the Texas Manufacturers' Association, an organization designed to promote productivity and business.
In 1956, the Graham family moved to Austin, where Callan took the position of executive director of the Texas Good Roads Association, lobbying for highway improvement and construction.
Duty called again however, and in 1986 Callan was asked to fill an unexpired term as Kimble County Attorney, the office that he was first appointed to fifty years earlier.