I think anyone can host a graduation party, as long as the terms of attendance are made clear. If you're hosting your own party, you pay for it. Graduations don't generally involve gifts, so it's not like a shower.
I can tell you about my own painful graduation experience when I got my master's degree. A friend of mine and her husband had offered to host a party for me. I said I'd leave planning the party up to them and I'd provide a guest list of people I wanted. My parents and other relatives were on the guest list. Several made the list only by courtesy (they were out-of-towners, and this was probably a faux pas of mine-my bad), but there were several family members who I thought had a reasonable shot at coming.
Turned out most of my relatives ignored the invitation (it was an eVite) and those who did pay any attention to it declined. (Among other problems, the day chosen for the party was Mother's Day.) It didn't help that my younger brother also got his master's degree at the same time and was set to graduate the same day. He chewed me out for choosing the same day. (This was the first I'd heard about it, and he came across as though that was my fault.) My mother, in her response to the eVite, blabbed about the conflict in dates. I seriously did not expect my parents to come to begin with as they live in Houston and I live in the Northeast.
My friend and I agreed to cancel the party and try to reschedule it, but we never rescheduled it. (I've never been able to reach her since except for job-hunting discussions.) So I didn't get a party or any kind of celebration at all. My family didn't care.