{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article1709","name":"A Deeper Investigation of PageRank as a Function of the Damping Factor","abstract":"PageRank is defined as the stationary state of a Markov chain. The chain is\r\n obtained by perturbing the transition matrix induced by a web graph with a\r\n damping factor $alpha$ that spreads uniformly part of the rank. The choice\r\n of $alpha$ is eminently empirical, and in most cases the original suggestion\r\n $alpha=0.85$ by Brin and Page is still used.\r\n In this paper, we give a mathematical analysis of PageRank when\r\n $alpha$ changes. In particular, we show that, contrarily to popular belief,\r\n for real-world graphs values of $alpha$ close to $1$ do not give a more\r\n meaningful ranking. Then, we give closed-form formulae for PageRank derivatives of\r\n any order, \r\n and by proving that the $k$-th iteration of the Power Method gives exactly the\r\n PageRank value obtained using a Maclaurin polynomial of degree $k$, we show\r\n how to obtain an approximation of the derivatives. Finally, we view PageRank\r\n as a linear operator acting on the preference vector and\r\n show a tight connection between iterated computation and derivation.","keywords":["PageRank","damping factor","Markov chains"],"author":[{"@type":"Person","name":"Boldi, Paolo","givenName":"Paolo","familyName":"Boldi"},{"@type":"Person","name":"Santini, Massimo","givenName":"Massimo","familyName":"Santini"},{"@type":"Person","name":"Vigna, Sebastiano","givenName":"Sebastiano","familyName":"Vigna"}],"position":3,"pageStart":1,"pageEnd":19,"dateCreated":"2007-06-28","datePublished":"2007-06-28","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Boldi, Paolo","givenName":"Paolo","familyName":"Boldi"},{"@type":"Person","name":"Santini, Massimo","givenName":"Massimo","familyName":"Santini"},{"@type":"Person","name":"Vigna, Sebastiano","givenName":"Sebastiano","familyName":"Vigna"}],"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.07071.3","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume641","volumeNumber":7071,"name":"Dagstuhl Seminar Proceedings, Volume 7071","dateCreated":"2007-06-28","datePublished":"2007-06-28","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article1709","isPartOf":{"@type":"Periodical","@id":"#series119","name":"Dagstuhl Seminar Proceedings","issn":"1862-4405","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume641"}}}