business-school, law-school, college, high-school (in the US), medical-school, university
job opportunities for university graduates

arts, engineering, history, law, medical, science, etc.
doctoral (AmE)
cum laude, magna cum laude, summa cum laude (all in the US)
Oxbridge (= from Oxford or Cambridge)
new, recent

course, degree, program (AmE)
education (AmE), studies, work
level
She has taught at both the undergraduate and graduate levels.

school (AmE)
student
assistant (esp. AmE)
recruit, trainee (both BrE)
He joined the company as a graduate trainee.

recruitment (BrE)
The company places great importance on graduate recruitment and training.

graduate in
a graduate in sociology

Graduate is used with these nouns as the subject:
cadet, class, college

Graduate is used with these nouns as the object:
college