Social and 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 9.3 Semi-Anonymous Graphical Games 273 9.4 Randomly Chosen Neighbors and Network Games 279 9.5 Richer Action Spaces 286 9.6 Dynamic Behavior and Contagion 293 9.7 Multiple Equilibria and Diffusion in Network Games 297 9.8 Computing Equilibria 304 9.9 Appendix: A Primer on Noncooperative Game Theory 308 9.10 Exercises 319 Chapter 10: Networked Markets 327 10.1 Social Embeddedness of Markets and Exchange 328 10.2 Networks in Labor Markets 334 10.3 Models of Networked Markets 353 10.4 Concluding Remarks 365 10.5 Exercises 366 PART IV: METHODS, TOOLS, AND EMPIRICAL ANALYSES Chapter 11: Game-Theoretic Modeling of Network Formation 371 11.1 Defining Stability and Equilibrium 372 11.2 The Existence of Stable Networks 377 11.3 Directed Networks 383 11.4 Stochastic Strategic Models of Network Formation 388 11.5 Farsighted Network Formation 395 11.6 Transfers and Network Formation 399 11.7 Weighted Network Formation 402 11.8 Agent-Based Modeling 406 11.9 Exercises 407 Chapter 12: Allocation Rules, Networks, and Cooperative Games 411 12.1 Cooperative Game Theory 412 12.2 Communication Games 416 12.3 Networks and Allocation Rules 419 12.4 Allocation Rules When Networks Are Formed 425 12.5 Concluding Remarks 430 12.6 Exercises 430 Chapter 13: Observing and Measuring Social Interaction 434 13.1 Specification and Identification 435 13.2 Community Structures, Block Models, and Latent Spaces 443 13.3 Exercises 457 Afterword 459 Bibliography 461 Index 491