It depends on the type of group. A large group, for example, the Democratic party, is focused predominantly around the presidential candidate. Obviously, he doesn't know everyone involved personally, but the reason that this group has gathered together, or even just perephally involved, is to get him elected.

But then you have a smaller scale, like, say, my dorm-mates and me. We all know one another, and the relationship isn't all based on solely one person.