Dr. Wu,
There are so many aspects of this one could discuss. One that I thought you might be getting at, when you modeled the facebook vs LinkedIn is the venue.
In my world, I see some of my community members not only have relationships within our community, but they also interact on other communities, read each other's blogs, follow and RT on twitter, and share content on facebook and comment or like what each other say there. They do this in different combinations. No doubt there are several more networks that they are on in various combinations which I'm not following. I can only keep up with a tiny fraction of the community and greater social eco-system. What does it look like?
Because I'm a simple kind of guy, I'm thinking about the social platform as a layer and seeing which members exist in each layer and how they interact (creating an edge?) and how those might stack up to form a 3 dimensional model. Quickly though, this gets beyond human ability to neatly diagram it out, or keep up with it in our head.
One could imagine how the Lithium platform might evolve to support this kind of model, to be able to visualize interactions within the community, into facebook, twitter, linkedIn - adding layers to the model.....
Mark