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.

About the Book

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.

The book gives an excellent introduction to various aspects of the Web graph and the mathematical techniques that can be applied to their exploration. I have recommended the book to my graduate students as an introduction to research on graph models, and found that the students appreciate its expository style. The book contains extensive problem sets, making it a good teaching tool. The book is largely self-contained, and lends itself well for a topics course in discrete mathematics. To my knowledge, this book is the best introduction for mathematics students to the exciting research that started with the study of the Web graph.

Overall the text is well-structured and pleasant to read for mathematically oriented readers and very fit to be taken as a text book also for a less mathematical audience. I personally eagerly await for the opportunity to give a course based on Bonato’s book at the postgraduate level.

Bonato’s book provides an introduction to the ongoing mathematically rigorous research on the properties of models for the web graph. It is well-suited for teaching a class on the matter to graduate students or advanced undergraduates.

This book will be a valuable source for mathematicians trying to get some idea of the developments relating to web graphs and similar networks.

The text is largely self-contained and would be suitable for self-study. This is a solid effort, well organized and clearly written.

The book is a readable and up-to-date exposition of the mathematical theory of web graphs and related real-world self-organizing networks.

Dr. Anthony Bonato is a globally recognised expert in graph theory and network science. He has authored over 150 papers and eight books, including Dots and Lines: Hidden Networks in Social Media, AI, and Nature (Johns Hopkins University Press, 2025).