This is what Google thought Google+ would be, but users were more about connecting to anyone and everyone and it became too messy for Google to want to deal with.
G+ was glorious in the beginning days. With no qualms it was the best social network I've experienced yet. IMO, what killed it was Google requiring the real names - which I still believe was a good idea - but then the death knell was when they waffled on that. If they would have stood firm on the real names policy, I'm convinced they would still be here today and there is a very good chance they would have surpassed both Facebook and Twitter.