University of the District of Columbia Graduate Programs Act - Amends the Higher Education Act to: (1) make the University of the District of Columbia (UDC) David A. Clarke School of Law and other UDC qualified graduate programs eligible for federal grants for postgraduate programs substantially contributing to the legal, medical, dental, veterinary, or other graduate education opportunities in mathematics, engineering, or the physical or natural sciences for black Americans; and (2) authorize appropriations for FY2008-FY2013 for such grant program.