Graham attended the University of North Carolina at Chapel Hill, where he studied law and was an active member of the Dialectic Society.

[4] In 1840, Graham was elected to the United States Senate as a Whig to fill the vacancy created by the resignation of Robert Strange.

[7] In December 1860, James Alexander Hamilton of New York made an abortive appeal to the Pennsylvania presidential electors that they vote for Graham for president as a possible means of preserving the Republic.

In April 1865, with the Confederacy near defeat, Graham personally led a delegation that included another former governor, David Swain, to ask Union General William T. Sherman for a truce so that the state's capital, Raleigh, might be spared violence and destruction.

[8][9] In 1866 Graham was once again elected to the United States Senate, but because North Carolina had not yet been readmitted to the Union, he could not present his credentials.

From 1867 to 1875, he was a member of the board of trustees of the Peabody Fund, which provided educational assistance to the post-Civil War South.