Being a graduate isn't as big as it may seem. Sure, you get that fancy W for Witch/Wizard, but that doesn't really do all that much. I propose a wall of graduates form Hogwarts, in order of graduation. So, for example, it'd be like. 1. Dayanara Lewis (Or whatever it is), 2. Blast Greengrass, and so on. This would encourage players to graduate, instead of sticking around at Year 7. This also puts an aspect of competition into it, because who doesn't want to be near the front of the list?
Anyway, that's just an idea, and why I put it here.