I don't think social networking has a business model. It is not an end goal, it is a feature that will (should!) be included in other applications.
Adding social networking features allows additional functions in your applications: group filtering, recommendations, trust models, reputation, identity and profile management. The identity management part is an area that could use a lot of work still.
Stuart Henshall is thinking about it, so I'm sure we'll get some good thoughts on it soon:
David Coursey chimes in to the Social Networking is Broken theme. So if it is broken with no business model where to next?
Social networks are a good thing. Everybody should have one--and everybody I know does, in some form or fashion. But whether you need an online social network and, particularly, whether you need one whose primary purpose is separating you from your money is another question entirely.
No Business in Social Networking
Where to?Unbound Spiral (Stuart Henshall): Forget Current Social Networking Models
This is a question I've been pondering I just know I'm not getting to it tonight. Maybe someone else in the network will.