Hello Ned,
Thank you for posting your question here. As you can already see in the comments, there are some really inquisitive readers here and some of the questions you asked on twitter have already been addressed, either directly or indirectly.
To your point on the indirect (2nd degree) connections as being part of your relationships, I would have to challenge you a bit on that. Since the social network connects everyone on this planet, you kind of have to make a cut off some where. I used a very strict cut off and considered only those that are directly connected to you as a your network. And those are the relationship that I considered truly your relationships.
As I understand it, you want to extend that to include 2nd degrees, and maybe even 3rd degrees. But my question then is why stop at 2nd (or 3rd) degree. Why not 3rd, or 4th. If you continue to follow that argument, then everyone is related to you, because everyone is only about 6 to 7 degrees apart from you. If you meet a friend of your friend and become friends with him/jher, then s/he would become a 1st degree (direct) connection. Besides (a minor point) what do you call the relation friends of friends? If you want to consider that as a valid relationship, why not have friends of friends of friends as a relationship as well. We certainly don't refer to people that way. If you know them they are your friends (your direct connection), if not they are not your friends, even if they are just 2 degrees away from you. You may know them from a friend, so you call them friend of friend, but the fact that you know them already implicitly implies that they are your friends now. Before you know them, you simply don't know them. Anyway, this is my rigorous view (part of my training as a mathematician). But feel free to challenge me...
Yes, the dynamics between communities and social netwroks is definitely very interesting, and it is a topic that I will write about in later post (actually they are already written). As in my reply to Mark_Kaufman, there is definitely a symbiotic relationship between the two. And your point about acquisition and retension is definitely on the right track. I'm glad you thought about it that way. It definitely reaffirms my research.
There are definitely a lot of loose ends given what I've posted now. Maybe I shouldn't split up my long-ish article into such short chunks of posts, and that it would be more clear to post the whole thing as one giant article. I have mix feeling about that though... I hope that as I publish the later posts, things will clear up as we go along.
I sincerely appreciate you taking the time to post the question here. Hope to see you next time.