At any rate, I'm sure everyone's familiar with the concept of "six degrees of separation" (which I think may be a terribly pessimistic number if you consider just the United States, considering I can get the last three presidents in at most two steps each, and I'm a bloody political nobody. If you're talking about the whole world, that might be a better number). And, of course, there's the "Bacon game" (whose topology, incidentally, we worked out over a game of soccer back in college. Don't ask). And the somewhat similar game of "Wikiwhacking" from one Wikipedia topic to another. I've idly thought about doing something similar with LJ users, but of course it's much more difficult to make linkages there. And I'm not so much interested in actually finding the links as much as wondering how long the farthest links are, and that sort of thing.
Of course, LJ does have the "friends of friends" page thing, and the "popular users amonst your friends" thing (which actually turned out to be useful for me, since I stumbled across a large chunk of people I knew -- but didn't know were on LJ -- recently), but nothing as developed as, say, Friendster has (where, incidentally, a quick check shows that I have 35k third-degree friends -- oh, how the mighty have fallen or, like, whatever. I like how it tells me that a grand total of one people have read my profile in the last seventeen days. Er, why seventeen days? Why not a week? Or a month? Nice to know that I'm still friends with Nyarlathotep and Cthulhu, though. Insanity was always the strongest bond.)
But, I think much more interesting (to the point of almost being practical) would be finding the other LJ users who had the same interests as you. A few weeks ago, I even wrote a quick-and-dirty HTML-grabbing perl script to do just that, but it's not really very practical. The problem is that when you do the "search for people by interest" thing, it only gives you on the order of 400-odd people and 400-odd communities, max, and given the eight million or so LJ users, it's not surprising that more popular interests such as "anime" or "linux" or "underwater basket weaving" tend to be overrun by early adopters, so those people tend to dominate the list my little program generates. I wonder if there's any way to get hooks into LJ that would return full lists for those things (I've seen things that show "most popular interests among your friends" and such, but I don't know if they were built by the LJ people themselves, or done in the same primitive brute-force way as my "interest-matching" program, and, well, that's a far less computationally-intensive thing to determine).
[On a completely unrelated note, I saw a program once that determined where all of your LJ "friends" were located geographically. I was wondering through some Canadian person's journal, and they'd noted that all of their American friends were -- to their evident approval -- in blue states. I thought it was amusing that while my friends are predominately people you'd associate with "blue-statism," I think only one of the ones who listed their location (in such a was as the program could parse it -- it couldn't handle locations that didn't include a city) was in a blue state. Make of that what you will.]