Since Matteo’s seminar about neighbourhood maps a couple of months ago I’ve been wondering whether PageRank could be applied to a local view of a social network to calculate trust scores. (This might be useful in the new darknet version of Freenet, for example.) One of the Freenet developers pointed out that PageRank is patented, but Wikipedia showed that using eigenvector centrality to calculate the importance of nodes isn’t a new idea.
After following a few references it turns out that the idea of propagating trust/status/etc across a graph dates back to at least 1953 . Pinski and Narin  suggested normalising each node’s output by dividing the output on each outgoing edge by the node’s outdegree. Geller  pointed out that their model was equivalent to a Markov chain: the scores assigned to the nodes followed the Markov chain’s stationary distribution. In other words, propagating trust/status/etc with normalisation at each node is equivalent to taking random walks from random starting points and counting how many times you end up at each node.
The only difference between Geller’s model and PageRank is the damping factor: in PageRank you continue your random walk with probability d or jump to a random node with probability 1-d. (Incidentally, when the algorithm’s described this way rather than in terms of a transition matrix, it’s easy to see how you could implement it on a web spider.)
 L. Katz, “A new status index derived from sociometric analysis,” Psychometrika 18 (1953), pp. 39-43. (PDF)
 G. Pinski and F. Narin, “Citation influence for journal aggregates of scientific publications: Theory, with application to the literature of physics,” Information Processing and Management 12 (1976), pp. 297-312. (PDF)
 N. Geller, “On the citation influence method of Pinski and Narin,” Information Processing and Management 14 (1978), pp. 93-95. (PDF)