Instead life is made up of piles and piles of little taxonomies used for specific purposes. I'm happy with that as both a mental model and a practical one.
I agree that the notion of a single social graph is an incoherent one, but Maciej's point is largely a quibbly one. There are graphs of human interactions that can be mapped out. These interaction graphs are not static. Data sets which purport to represent reality require updating, as they are not the canonical source.
But so what? That's true for maps of physical locations too, or article quality on wikipedia. Facebook shows, if nothing else, that it's possible to not just track but mediate (and still track) these interaction spaces for users as an end to itself (even if they are the product not the customers).
Does it matter that Facebrick isn't a perfectly synced representation of reality? Well, does it matter that Wikipedia isn't a totally accurate encyclopedia? You'd be right to ask for what cause, and to what end.
And that's the whole point. We dig up or create the little taxonomies that bridge the gaps that we're looking to cross.
Being social is all about disorganization, spontaneity, creativity, breaking out of all the stupid taxonomies that we impose on other people and have imposed on us. Trying to organize socialization to the extent that a "social graph" can be created is a profoundly sociopathic act. To push this task on users so that they do all the shoeboxing and tagging and linking, all in the name of "fun," requires some coercive force. It is no surprise that many Facebook users say that they don't really enjoy using it, but they have to. Part of that was the site's smart choice to maintain real names, so that you are always fretting about your online appearance. It's not a "perfectly synced representation of reality," but it is presented as such, almost like your own personal Wikipedia page, and by the laws of social anxiety you are compelled to check up on it! Shoebox, tag, link...
The line about Facebook rarely producing creative or original material really hit home for me. 4chan and SA are creative because they are fundamentally disorganized, and this freedom produces real moments of brilliance (and plenty more of profound stupidity). Facebook and its ilk are like corporate jobs disguised as consumer web products. You are constantly being shuffled from box to box, task to task, and the blinders have to be tightened ever so constantly to keep you from realizing why what you are doing really never will be "fun" in the way that a raucous party is fun.
About those blinders: those are in a big way the "privacy options" that every social network touts. Maciej points out, and I think that it's a salient point, that if everybody was able to see the whole social graph, it would dissolve. That alone should suggest that the social graph is an unnatural concept. Yet there is somebody, the owner of the social network, that can indeed see the entire graph, and there is a whole level of misdirection that they must apply to make this seem completely normal.
Again, maciej said most of this better than I could, so I'm glad he did.
That is a very euro-centric, post-modernist way of thinking.
What are caste system if not social?
What are far-flung familial relations if not social?
A definition of being "social" which only applies to societies where friendship is paramount, and friends come and go with ease is too limiting and leads you to solutions that can be awkward in other societies.
For example, in my country, we care deeply about family and ancestory--so much so that in every generation one member of the family is nominated to be the "memory keeper" (sorry, there's no translatable word) who keeps track of the geneology of everyone, and is expected at a glance to determine if a stranger is at least vaguely related to us.
Would a free form social graph be useful to us---not really. Our facebook pages are practically 90% family members, 10% people who through marriage will become family members.
You're right, even the way I defined "social" is too limited. But that irony only helps my point. You cannot define social, but this is precisely what the "social graph" is attempting to do. As soon as you create a definition, people react to it and oftentimes rebel against it. And then you are right back to the drawing board.
It's not about creating perfect Platonic models. It's about making cool things that people find useful. If you are trying to design a system that scaled to every single possible interaction from scratch then you've already failed, you can't compete with reality at that one.