COMP4121 Lecture Notes The PageRank, Markov chains and the Perron Frobenius theory LiC: Aleks Ignjatovic
[email protected] THE UNIVERSITY OF NEW SOUTH WALES School of Computer Science and Engineering The University of New South Wales Sydney 2052, Australia Topic One: the PageRank Please read Chapter 3 of the textbook Networked Life, entitled \How does Google rank webpages?"; other references on the material covered are listed at the end of these lecture notes. 1 Problem: ordering webpages according to their importance Setup: Consider all the webpages on the entire WWW (\World Wide Web") as a directed graph whose nodes are the web pages fPi : Pi 2 WWW g, with a directed edge Pi ! Pj just in case page Pi points to page Pj, i.e. page Pi has a link to page Pj. Problem: Rank all the webpages of the WWW according to their \importance".1 Intuitively, one might feel that if many pages point to a page P0, then P0 should have a high rank, because if one includes on their webpage a link to page P0, then this can be seen as their recommendation of P0. However, this is not a good criterion for several reasons. For example, it can be easily manipulated to increase the rating of any webpage P0, simply by creating a lot of silly web pages which just point to P0; also, if a webpage \generously" points to a very large number of webpages, such \easy to get" recommendation is of dubious value. Thus, we need to refine our strategy how to rank webpages according to their \importance", by doing something which cannot be easily manipulated \locally" (i.e., by any group of people who might collude, even if such a group is sizeable).