PageRank revisited

PageRank, one part of the search engine Google, is one of the most prominent link-based rankings of documents in the World Wide Web. Usually it is described as a Markov chain modeling a specific random surfer. In this article, an alternative representation as a power series is given. Nonetheless, it is possible to interpret the values as probabilities in a random surfer setting, differing from the usual one.Using the new description we restate and extend some results concerning the convergence of the standard iteration used for PageRank. Furthermore we take a closer look at sinks and sources, leading to some suggestions for faster implementations.