There are 3 US Post Offices in Graham County serving a total of 8,945 residents equating to 2,982 residents per post office. It's estimated that approximately 14,277 packages are handled across the 3 county post offices annually. Graham County is a county located in the U.S. state of North Carolina. As of the 2010 census, the population was 8,861, making it the third-least populous county in North Carolina. Its county seat is Robbinsville. The county was formed January 30, 1872, from the northeastern part of Cherokee County. It was named for William A. Graham, United States Senator from North Carolina (1840\u20131843) and Governor of North Carolina (1845\u20131849)."