Over 700 companies have gone on through YC, so they now have a few thousand alums and actively maintain an Alumni network -- really wish universities had something like this!
The companies go through the program in cohorts for a set amount of time -- they call these "classes". Not sure if universities have anything of the sort.
Sam Altman himself said that soon he "we will have to do something" with respect to housing. Again, nothing like I've seen any university do.
My personal favorite, though, is the part where they get everyone to come to dinner together to exchange experiences and whatnot. If only Harvard figured out that they could use their beautiful dining hall for this sort of thing...