Preface The internet affects many aspects of our lives, such as how we store and retrieve information, conduct business, and communicate. For example, in- formation is no longer only stored in printed form, but is represented on-line via a complex set of interconnected web pages. The web graph has vertices representing web pages, with edges corresponding to the links between pages. The web graph is a real-world network which has undergone intensive study in the last decade by theoreticians and experimentalists. Does this graph have interesting properties? Are there good, rigorous mathematical models for these properties? Can we exploit the graph structure of the web to help search it for information? The answer to all three questions is, of course, yes! The study of the web graph, or internet mathematics as it is now of- ten called, is an active field of study. As the subject is new, there is often a lack of consensus on the central topics, models, even notation, with key questions not always evident. As the subject is fast-breaking, a large arse- nal of techniques are required to model and analyze properties of the web. However, possessing the right mathematical tools and a familiarity with current research developments is an important first step. This book should supply a solid mathematical introduction to internet mathematics, and will encourage interest in an emerging and fascinating area of graph theory and theoretical computer science. The book resulted from lecture notes for an Atlantic Association for Research in the Mathematical Sciences (AARMS) Summer School graduate course Massive Networks and Internet Mathematics taught in July 2006 at Dalhousie University in Halifax. A version of the course was taught twice IX

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