[2] Graham County composes the Safford, Arizona Micropolitan Statistical Area.

The county is home to several organizations including Eastern Arizona College and the Mount Graham International Observatory, which includes one of the world's largest and most powerful telescopes.

[3] Graham County contains part of the San Carlos Apache Indian Reservation.

Joseph Knight Rogers, an early settler in the area, and a member of the Arizona Territorial Legislature, is known as the father of Graham County: he introduced the bill in the territorial legislature creating it.

[5] Initially, the county seat was located in the city of Safford but was later moved to Solomonville in 1883.

This change was undone in 1915, returning the county seat to Safford.

[16] As of the census of 2000, there were 33,489 people, 10,116 households, and 7,617 families living in the county.

20.9% of all households were made up of individuals, and 9.9% had someone living alone who was 65 years of age or older.

No Democratic presidential nominee has carried Graham County since Lyndon B. Johnson – against Arizona native Barry Goldwater – did so in 1964, though Bill Clinton, who carried significant national rural appeal as a Democrat in the 1990s, came close in 1996.

[18] The population ranking of the following table is based on the 2010 census of Graham County.