I've managed closed Fb group for ten years now. For new members we have a voting system in place. Inviting wouldn't work because if members could invite whoever they choose it will sooner or later lead to having members that not everybody is comfortable with. A friend of my friend may not necessarily be my friend. It'll create friction and lead to all sorts of interpersonal problems and soon enough it's not a peaceful community anymore, people start to block each other or lash out in comments just because their personalities or beliefs clash. I don't believe in invites anymore.

Google Wave and Googl+ also had invite system, it didn't work out well. Gmail is exception to the rule I'd say.