William Graham Swan (1821 – April 18, 1869) was an American attorney and politician active primarily in East Tennessee during the mid-19th century. Swan served in the Confederate States Congress during the American Civil War, and served one term as mayor of Knoxville, Tennessee, from 1855 until late 1856. He also helped establish the town of East Knoxville (later annexed by Knoxville), and served as its first mayor in the late 1850s. In 1854, Swan and his brother-in-law, Joseph Mabry, donated the initial land for the formation of Market Square in downtown Knoxville.