<p>I think you need to add the National Security Advisor and NSC Chairman to the list. He comes form a third track which is former military where he was once the Commander of NATO.
Office/ Undergrad / Grad-professional degree/ Political base-network</p>
<p>Secretary of State / Wellesley / Yale Law / Arkansas, DC & New York*
Treasury Secretary / Dartmouth / Johns Hopkins / DC & New York
Defense Secretary / William & Mary / Indiana & Georgetown / DC
Attorney General / Columbia / Columbia Law / DC
Interior Secretary / Colorado College / Michigan Law / Colorado*
Ag Secretary / Hamilton / Albany Law / Iowa*
Commerce Secretary / Yale / BU Law / Washington State*
Labor Secretary / Cal Poly Pomona / Southern Cal / California*
HHS Secretary / Trinity Washington / U Kansas / Kansas*
HUD Secretary / Harvard / Harvard / DC & New York
Transportation Secretary / Bradley / none / Illinois*
Energy Secretary / U Rochester / UC Berkeley / academia
Education Secretary / Harvard / none / Illinois
VA Secretary / West Point / Duke, National War College/ military
Homeland Security Secretary / Santa Clara / UVA Law / Arizona*
Council of Econ. Advisers Chair / William & Mary / MIT / academia
EPA Administrator / Tulane / Princeton / New Jersey
OMB Director / Princeton / LSE / DC
US Trade Representative / Austin College / UT-Austin Law/ Texas*
UN Ambassador / Stanford / Oxford / DC
Chief of Staff / Sarah Lawrence / Northwestern / DC & Illinois
National Security Advisor and NSC Chairmen/Georgetown/Military</p>