Social & Economic Networks

Preface xi PART I: BACKGROUND AND FUNDAMENTALS OF NETWORK ANALYSIS Chapter 1 Introduction 3 1.1 Why Model Networks? 3 1.2 A Set of Examples 4 1.3 Exercises 17 Chapter 2: Representing and Measuring Networks 20 2.1 Representing Networks 20 2.2 Some Summary Statistics and Characteristics of Networks 30 2.3 Appendix: Basic Graph Theory 43 2.4 Appendix: Eigenvectors and Eigenvalues 49 2.5 Exercises 51 Chapter 3: Empirical Background on Social and Economic Networks 54 3.1 The Prevalence of Social Networks 55 3.2 Observations on the Structure of Networks 56 PART II: MODELS OF NETWORK FORMATION Chapter 4: Random-Graph Models of Networks 77 4.1 Static Random-Graph Models of Random Networks 78 4.2 Properties of Random Networks 86 4.3 An Application: Contagion and Diffusion 105 4.4 Distribution of Component Sizes 107 4.5 Appendix: Useful Facts, Tools, and Theorems 110 4.6 Exercises 121 Chapter 5: Growing Random Networks 124 5.1 Uniform Randomness: An Exponential Degree Distribution 125 5.2 Preferential Attachment 130 5.3 Hybrid Models 134 5.4 Small Worlds, Clustering, and Assortativity 141 5.5 Exercises 150 Chapter 6: Strategic Network Formation 153 6.1 Pairwise Stability 154 6.2 Efficient Networks 157 6.3 Distance-Based Utility 159 6.4 A Coauthor Model and Negative Externalities 166 6.5 Small Worlds in an Islands-Connections Model 170 6.6 A General Tension between Stability and Efficiency 173 6.7 Exercises 179 PART III: IMPLICATIONS OF NETWORK STRUCTURE Chapter 7: Diffusion through Networks 185 7.1 Background: The Bass Model 187 7.2 Spread of Information and Disease 189 7.3 Search and Navigation on Networks 209 7.4 Exercises 221 Chapter 8: Learning and Networks 223 8.1 Early Theory and Opinion Leaders 224 8.2 Bayesian and Observational Learning 225 8.3 Imitation and Social Influence Models: The DeGroot Model 228 8.4 Exercises 253 Chapter 9: Decisions, Behavior, and Games on Networks 257 9.1 Decisions and Social Interaction 258 9.2 Graphical Games 269

Matthew O. Jackson is the William D. Eberle Professor of Economics at Stanford University.

"Lucid and comprehensive, Jackson's book elegantly synthesizes several important strands of network science from sociology, physics, mathematics, computer science, and economics. It will be an immensely useful reference for researchers and students alike."--Duncan Watts, Columbia University