Google PageRank as mean playing time for pinball on the reverse web

It is known that the output from Google’s PageRank algorithm may be interpreted as (a) the limiting value of a linear recurrence relation that is motivated by interpreting links as votes of confidence, and (b) the invariant measure of a teleporting random walk that follows links except for occasional uniform jumps. Here, we show that, for a sufficiently frequent jump rate, the PageRank score may also be interpreted as a mean finishing time for a reverse random walk. At a general step this new process either (i) remains at the current page, (ii) moves to a page that points to the current page, or (iii) terminates. The process is analogous to a game of pinball where a ball bounces between pages before eventually dropping down the exit chute. This new interpretation of PageRank gives another view of the principle that highly ranked pages will be those that are linked into by highly ranked pages that have relatively few outgoing links. 1 The PageRank System Google’s PageRank algorithm [6] assigns an importance ranking to each known web page. This information may then be used by a search engine that seeks to find relevant and important matches for a user’s query. Suppose there are N This manuscript appears as University of Strathclyde Mathematics Research Report 15 (2004). Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, UK. Supported by a Research Fellowship from The Royal Society of Edinburgh/Scottish Executive Education and Lifelong Learning Department.