Graham was born and raised in Washington County, Kentucky. He studied English and became a schoolteacher, moving to Hancock County, Illinois, in 1836 to teach. He returned to Washington County, Kentucky, and in 1839 or 1840 ran an unsuccessful campaign for state representative in the Kentucky General Assembly.
Graham was raised in Washington County, Kentucky, where he studied English and became a teacher. He then moved to Hancock County, Illinois, in 1836 to teach, before returning to Washington County, Kentucky, and attempting to secure a position as a state representative in the Kentucky General Assembly in 1839 or 1840.