Same-sex marriage advocates argue that the clause of the constitution means that legally sanctioned same-sex marriages performed in one state should automatically be recognized by other states.

The answer that best completes the statement above is this: full faith and credit. The Full Faith and Credit Constitution is found in the Article IV, Section 1 of the United States Constitution. This states that whatever public actions and judicial proceedings that are practiced by every state should be respected by other states. In this case, it is the same-sex marriage issue which are being promoted by the advocates. 

An informal structure in a bureaucracy would be something like so-called "office politics". where there's a formal structure set up for the organization, but then an informal subculture as well that has a way of organizing the bureaucracy further. this can be positive because it sets up an added degree of organization, albeit informal, within the bureaucracy.