Graham played bass in the highly successful and influential funk band Sly & the Family Stone from 1967 to 1972. It is said that he pioneered the art of slap-pop playing on the electric bass, in part to provide percussive and rhythmic elements in addition to the notes of the bass line when his mother's band lacked a drummer; the slap of the thumb being used to emulate a bass drum and the pop of the index or middle finger as a snare drum. This style has become archetypal of modern funk. Slap-pop playing couples a percussive thumb-slapping technique of the lower strings with an aggressive finger-snap of the higher strings, often in rhythmic alternation. The slap and pop technique incorporates a large ratio of muted (or 'ghost' tones) to normal notes, which adds to the rhythmic effect.
This "Slap" bass style was later used by such artists as Les Claypool, Bootsy Collins, Louis Johnson, Mark King, Flea, Victor Wooten, Marcus Miller, Stanley Clarke, John Norwood Fisher, P-Nut, Danny McCormack, Matt Noveskey, Dirk Lance, and Kenny Franklin (of San Mateo).
Upon the Family Stone's disintegration due to lead singer Sly Stone's drug addiction, Graham formed his own band, Graham Central Station. The name is a pun on Grand Central Station, the train station located in the Manhattan borough of New York City. Graham Central Station had several hits in the 1970s, including "Hair."