Spending on universities is usually justified by the “graduate premium”—the increase in earnings that graduates enjoy over non-graduates. 

这个定语从句改为独立分句则为：

Graduates enjoy the increase in earnings over non-graduates.

= The increase in earnings is an advantage of graduates over non-graduates.

《韦氏高级词典》对over这个意义的解释和例句如下：

— used to say that a person or thing is better than (someone or something else)

• The new model has several advantages over the old one.

• This is a big improvement over our last apartment.

• I would choose you over any other woman in the world.

所以，over介词短语在原句中作状语，修饰enjoy。

句义为：研究生享有研究生奖学金，而非研究生则没有。