There’s a rather nice meme and lj toy that’s currently doing the rounds, that examines your friends list to find the largest cliques (groups of mutual friends). I considered writing something similar myself a few months ago, but had to put it to one side due to a lack of free time. A really interesting adjunct to this service would be a service that identifies the articulation points that link different cliques. A really really interesting service would correlate the results with the interest lists of the members of a clique in order to try and work out the common interests of the clique.
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