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Graduation is the method of earning fame in Valthirian Arc.
The first thing you need to know about graduating a student is that they do not have to be rank 30. You can assign any students to your Academy and hand them a diploma as soon as they walk in the door if you want; they just won't be worth much fame for your Academy.
Five or six things affect the fame value of a graduating student: class, rank (questionable), stats (proven, but not put to an equation), # of quests completed, weapon grade, and if they're the class on demand this month.
The class on demand on Month 1, Year 1 is always a base one.
When graduating students around level 10, unless there there is a particular class on demand asked for in the Academy screen, do not convert your students to another class yet. This is especially true if you are very close to not achieving your fame goal.
Because of the 1.3x modifier for fame for the base classes, conversion of first tier classes characters to second tier classes often results in a loss of fame.
Please notice that a first tier class, when on demand grants a (1.3x1.5) = 1.95 modifier.