A course on the Web graph / Anthony Bonato.

Format:

Book

Author/Creator:

Bonato, Anthony, 1971- author.

Series:

Graduate studies in mathematics ; v. 89.

Graduate studies in mathematics ; volume 89

Language:

English

Subjects (All):

Internet--Mathematical models.

Internet.

Telecommunication--Traffic--Mathematical models.

Telecommunication.

Representations of graphs.

Information visualization.

Physical Description:

1 online resource (200 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society ; [Nova Scotia, Canada] : Atlantic Association for Research in the Mathematical Sciences, [2008]

Language Note:

English

Summary:

'A Course on the Web Graph' provides an introduction to state-of-the-art research on the applications of graph theory to real-world networks such as the Web graph. It discusses both models of the web graph and algorithms for searching the web.

Contents:

""Cover""; ""Title""; ""Copyright""; ""Contents""; ""List of Figures""; ""Preface""; ""Chapter 1. Graphs and Probability""; ""Â1.1. Introduction""; ""Â1.2. Graph Theory""; ""Â1.3. Probability Theory""; ""Exercises""; ""Chapter 2. The Web Graph""; ""Â2.1. Introduction""; ""Â2.2. Other Real-World Self-Organizing Networks""; ""Exercises""; ""Chapter 3. Random Graphs""; ""Â3.1. Introduction""; ""Â3.2. What is a Random Graph?""; ""Â3.3. Expectation and the First Moment Method""; ""Â3.4. Variance and the Second Moment Method""; ""Â3.5. Martingales and Concentration""; ""Exercises""

""Chapter 4. Models for the Web Graph""""Â4.1. Introduction""; ""Â4.2. On-Line Web Graph Models""; ""Â4.3. Future Challenges in Modelling the Web Graph""; ""Exercises""; ""Chapter 5. Searching the Web""; ""Â5.1 Introduction""; ""Â5.2 An Overview of Search Engines""; ""Â5.3 Adjacency Matrices and the Perron-Frobenius Theorem""; ""Â5.4 Markov Chains""; ""Â5.5 PageRank""; ""Â5.6 HITS""; ""Â5.7 SALSA""; ""Â5.8 Further Analysis of Web Ranking Algorithms""; ""Exercises""; ""Chapter 6. The Infinite Web""; ""Â6.1 Introduction""; ""Â6.2 The Infinite Random Graph""

""Â6.3 Representations and Properties of R""""Â6.4 Limits of Copying Models""; ""Â6.5 Limits of Preferential Attachment Models""; ""Â6.6 The n-Ordered Graphs and Their Limits""; ""Exercises""; ""Chapter 7. New Directions in Internet Mathematics""; ""Â7.1 Introduction""; ""Â7.2 Eigenvalues of Power Law Graphs""; ""Â7.3 Modelling Viruses on the Web""; ""Â7.4 Dominating Sets in the Web Graph""; ""Exercises""; ""Bibliography""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""J""; ""K""; ""L""; ""M""; ""N""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""

""Back Cover""

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 171-180) and index.

Description based on print version record.

ISBN:

1-4704-2119-4