Hello Mark,
Thank you for the comment...
What you said is very true. The community is only one channel for people to interact. So we only see a subset of the people’s social network through the community. Thus, we only see a subset of relationships there.
This is exactly the same situation in the real world. For example, our colleagues only see the relationship that we establish at work: who is my teammates, who works under me, who is my manager, etc. But they may not see our family-relationship or our friend-relationship, unless that colleague also happen to be a friend of your as well.
That is the reason why we are creating the social engagement center (Some of you out there are already on the beta program for this product feature). The hope is that we can see some slices of the relationship across different social media channels that are relevant to a brand or a company.
I agree that visualizing the social network beyond communities may be very nice, but I am certain if that will be very useful or meaningful. Because, as we learned from social anthropology that human have an inherent limit on how many relationships they can keep track. This limit is known as the Dunbar's number, which is around 150. It says that human can only keep track of ALL the relationships among 150 people. Today social media appears to increase the number of relationships that we can maintain, but our brain did not changed. We simply know less about each relationship.
But that is OK, in most case we only need to know the tiny but relevant bits of relationships about someone. At work we only need to know about our colleagues work-related relationships, and we do not need to know about their family and friends. That is why social media, social network sites and communities focus on only one specific relationship at a time (i.e. Facebook is for friendship, LinkedIn is for work-business related relationships, communities are for relationships that is form by a common interest).
If we try to overlay the relationship for all social media channels, that social graph would not be readable. You can see that with my toy example in this post. Even with an overly simplistic social network of my 7 hypothetical friends that only have 3 kinds of relationships, the social graph of my entire social network is an overlay of my LinkedIn social graph, my beer buddy graph, and my badminton pal graph. If I want to keep all these relationships visible, we get (figure 1), which is kind of hard to read. If we collapse all these relationship together and just call them friendship, then we get (figure 2a). But you also lose the detail information about who is colleague, who is beer buddy, and who is your badminton pal.
It really is a tradeoff of how much detail you want to know about how many people. It is not possible to know a lot of details for all people. Our brains just cannot process that much information, even if we can visualize them.
Moreover, we can't really vizualize everything at once. Think about this: Facebook has 400 million users, your computer monitor don’t even have enough pixels to display a tiny fraction of the users in that network (even if you represent each user as 1 pixel dot). If we want to draw all the lines connecting between all the dots, the whole screen would be pitch black full of all the edges on top of each other, which is clearly meaningless and useless.