Google's PageRank and Beyond

Preface ix Chapter 1: Introduction to Web Search Engines 1 1.1 A Short History of Information Retrieval 1 1.2 An Overview of Traditional Information Retrieval 5 1.3 Web Information Retrieval 9 Chapter 2: Crawling, Indexing, and Query Processing 15 2.1 Crawling 15 2.2 The Content Index 19 2.3 Query Processing 21 Chapter 3: Ranking Webpages by Popularity 25 3.1 The Scene in 1998 25 3.2 Two Theses 26 3.3 Query-Independence 30 Chapter 4: The Mathematics of Google's PageRank 31 4.1 The Original Summation Formula for PageRank 32 4.2 Matrix Representation of the Summation Equations 33 4.3 Problems with the Iterative Process 34 4.4 A Little Markov Chain Theory 36 4.5 Early Adjustments to the Basic Model 36 4.6 Computation of the PageRank Vector 39 4.7 Theorem and Proof for Spectrum of the Google Matrix 45 Chapter 5: Parameters in the PageRank Model 47 5.1 The alpha Factor 47 5.2 The Hyperlink Matrix H 48 5.3 The Teleportation Matrix E 49 Chapter 6: The Sensitivity of PageRank 57 6.1 Sensitivity with respect to alpha 57 6.2 Sensitivity with respect to H 62 6.3 Sensitivity with respect to vT 63 6.4 Other Analyses of Sensitivity 63 6.5 Sensitivity Theorems and Proofs 66 Chapter 7: The PageRank Problem as a Linear System 71 7.1 Properties of (I -- alphaS) 71 7.2 Properties of (I -- alphaH) 72 7.3 Proof of the PageRank Sparse Linear System 73 Chapter 8: Issues in Large-Scale Implementation of PageRank 75 8.1 Storage Issues 75 8.2 Convergence Criterion 79 8.3 Accuracy 79 8.4 Dangling Nodes 80 8.5 Back Button Modeling 84 Chapter 9: Accelerating the Computation of PageRank 89 9.1 An Adaptive Power Method 89 9.2 Extrapolation 90 9.3 Aggregation 94 9.4 Other Numerical Methods 97 Chapter 10: Updating the PageRank Vector 99 10.1 The Two Updating Problems and their History 100 10.2 Restarting the Power Method 101 10.3 Approximate Updating Using Approximate Aggregation 102 10.4 Exact Aggregation 104 10.5 Exact vs. Approximate Aggregation 105 10.6 Updating with

Amy N. Langville is Assistant Professor of Mathematics at the College of Charleston in Charleston, South Carolina. She studies mathematical algorithms for information retrieval and text and data mining applications. Carl D. Meyer is Professor of Mathematics at North Carolina State University. In addition to information retrieval, his research areas include numerical analysis, linear algebra, and Markov chains. He is the author of "Matrix Analysis and Applied Linear Algebra".

Honorable Mention for the 2006 Award for Best Professional/Scholarly Book in Computer & Information Science, Association of American Publishers "[F]or anyone who wants to delve deeply into just how Google's PageRank works, I recommend Google's PageRank and Beyond."--Stephen H. Wildstrom, BusinessWeek "This is a worthwhile book. It offers a comprehensive and erudite presentation of PageRank and related search-engine algorithms, and it is written in an approachable way, given the mathematical foundations involved."--Jonathan Bowen, Times Higher Education Supplement "This book should be at the top of anyone's list as a must-read for those interested in how search engines work and, more specifically how Google is to meet the needs of so many people in so many ways."--Michael W. Berry, SIAM Review "Amy N. Langville and Carl D. Meyer examine the logic, mathematics, and sophistication behind Google's PageRank and other Internet search engine ranking programs... It is an excellent work."--Ian D. Gordon, Library Journal "If I were taking, or teaching, a course in linear algebra today, this book would be a godsend."--Ed Gerstner, Nature Physics "Langville and Meyer present the mathematics in all its detail... But they vary the math with discussions of the many issues involved in building search engines, the 'wars' between search engine developers and those trying to artificially inflate the position of their pages, and the future of search-engine development... Google's PageRank and Beyond makes good reading for anyone, student or professional, who wants to understand the details of search engines."--James Hendler, Physics Today "This book is written for people who are curious about new science and technology as well as for those with more advanced background in matrix theory... Much of the book can be easily followed by general readers, while understanding the remaining part requires only a good first course in linear algebra. It can be a reference book for people who