Every Tiki User has the option of creating their own user page (which is a Wiki page with special permissions), if you allow that option. There is also the "friendship network" which is a rather lacking/neglected feature but it allows you to request friendship of other Tiki users.
Oh and if you want to, you can collect some additional information from users at registration time, for example favorite color, favorite artists, favorite movie (which seems like a very social network thing to do). Users can optionally be allowed to change their own recorded information.
 It just occurred to me that each user could have his/her own blog which could function as a sort of "Wall", to which other users could post comments.
This is basic Facebook-type-behaviour, or are you talking about some kind of Facebook integration?