A Course on the Web Graph
About this Title
Anthony Bonato, Ryerson University, Toronto, ON, Canada
Publication: Graduate Studies in Mathematics
Publication Year 2008: Volume 89
ISBNs: 978-0-8218-4467-0 (print); 978-1-4704-2119-9 (online)
MathSciNet review: MR2389013
MSC: Primary 05-01; Secondary 05C80, 05C90, 68R10, 94C15
A Course on the Web Graph provides a comprehensive introduction to state-of-the-art research on the applications of graph theory to real-world networks such as the web graph. It is the first mathematically rigorous textbook discussing both models of the web graph and algorithms for searching the web.
After introducing key tools required for the study of web graph mathematics, an overview is given of the most widely studied models for the web graph. A discussion of popular web search algorithms, e.g. PageRank, is followed by additional topics, such as applications of infinite graph theory to the web graph, spectral properties of power law graphs, domination in the web graph, and the spread of viruses in networks.
The book is based on a graduate course taught at the AARMS 2006 Summer School at Dalhousie University. As such it is self-contained and includes over 100 exercises. The reader of the book will gain a working knowledge of current research in graph theory and its modern applications. In addition, the reader will learn first-hand about models of the web, and the mathematics underlying modern search engines.
Graduate students and research mathematicians interested in graph theory, applied mathematics, probability, and combinatorics.
Table of Contents
- Chapter 1. Graphs and probability
- Chapter 2. The web graph
- Chapter 3. Random graphs
- Chapter 4. Models for the web graph
- Chapter 5. Searching the web
- Chapter 6. The infinite web
- Chapter 7. New directions in internet mathematics