Maybe we're making some progress:

So, we started with social graphs, social media, and social search (below I refer to these three as 'social X') and asked the questions about purposes, the utility of social X, and the means to the purposes.

For entertainment, there is a huge industry from movies and TV. One lesson is, high quality content with broad appeal is expensive to produce. In particular I don't see Internet social X doing much better at generating good entertainment content.

I will insert another point: The more such good entertainment is produced, the more expensive it is to produce even better entertainment. So, we should be moving to about enough high quality digital recordings of such entertainment to satisfy anyone for life and, thus, have less pressing reasons to produce more.

You mentioned:

"This data is usually used as you stated to find similarities . In people, for matchmaking sites, here are things purchased by people who...read the same stuff, watch the same movies, etc. It can turn out well, but for what was known by the Netflix challenge teams as the Napoleon Dynamite problem. A movie that based on similarity clusters was almost impossible to predict how a user would rate it."

I can believe that! Apparently the idea was that persons A and B are 'similar' and person A likes movie X so that then maybe person B will also like movie X. That is not promising because the 'connections' are too crude: E.g., two sisters can be very close yet be very different in the movies, music, clothes, boys, etc. they like.

It appears that the Netflix people fell into a trap: Apparently commonly in the literature of 'collaborative filtering', 'recommendation engines', and 'data mining' has been the suggestion that we should start by putting people into 'clusters' and for each cluster observe what movies, music, etc. were popular in that cluster. Then, given another person, say, a user, find what cluster they were in and then recommend to them what was popular in that cluster. Not a good idea. Interesting to hear that the idea failed!

So, we might conclude that some of the data for such clustering, recommending, etc. can be represented as social graphs, but that step appears to be just a tangential afterthought and not a good example of the utility of social graphs.

Yes, people like to communicate and form communities: Significant examples from the past include back fences, kitchen tables for coffee, lunches, dates, parties, various meetings (e.g., PTA, alumni, school board, political parties, church), school, and work. Such conversations and communities have been significant for romance, building a business, getting a job, education, skills, arts, crafts, politics, and more. But I'm failing to see that the communities that result from Internet social X are very significant.

Net, I don't see current Internet social X doing very well on entertainment, conversations, or communities.

I see the Internet as terrific for a lot, e.g., news, short video clips, technical information, the content on Wikipedia, general information on organizations, information from topical blogs and long tail Web sites, shopping, and more. But so far I don't see social media as leading to very significant utility.

Then in particular I don't see much value in the data on social graphs.

Still, Facebook has 500+ million users and is worth maybe over $50 billion; Twitter, Foursquare, etc. are significant; and Page believes that 99% of social search has yet to be done.

So, here we can look at the weakness in social X, and that might mean that there is an opportunity to do better and have some astounding success. Or, a guess is that current social media efforts are not really addressing the fundamental purposes and opportunities very directly or well so that a better effort could be quite successful.