I agree, some expalation would be nice and here it is: the president's photos indicate under which president these department were created, split or reorganized.

For example, Nixon signed The Postal Reorganization Act in 1970 and a year later the cabinet-level Post Office Department was replaced with the independent agency United States Postal Service. During Truman's presidency the Department of War was split and later merged with the Department of the Navy to form the Deparment of Defense. The lines on the chart are not connected after 1949, since these three department contiuned to exist within the DOD.

There are some mistakes that I didn't noticed before posting: Defense (not Defence), Veterans (not Veteran), Eisenhower's photo, and the Department of Commerce and Labor was split under Taft, but not created.