Our "home" addresses are linked between parent and student. When a student graduates, should the sharing link be broken?  Should be keep the link and create a "college" address and make it primary? 

You do not need to break the link with the address as you can choose to copy preferred to alternate address.  This will change the address type to previous and end date the address.  You can then enter their new address and save this as the preferred. 

You will not want to delete it in order to preserve a historical backtrack of the different addresses a person has lived.  Furthermore, more than likely when the student graduates they will be returning to their parents address anyway.