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We provide the analysis of the Google PageRank from the perspective of the Markov Chain Theory. First we study the Google PageRank for a Web that can be decomposed into several connected components which do not have any links to each other. We show that in order to determine the Google PageRank for a completely decomposable Web, it is sufficient to compute a subPageRank for each of the connected components separately. Then, we study incentives for the Web users to form connected components. In particular, we show that there exists an optimal linking strategy that benefits a user with links inside its Web community and in contrast inappropriate links penalize the Web users and their Web communities. We conclude by giving practical recommendation on how to improve a personal Page Rank.
This is a joint work with N. Litvak from the University of Twente.
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