The growth of Facebook exemplifies our connectedness. How do connected systems operate? This book beautifully explains the underlying ideas to a broad student audience and would be fascinating to many readers. The authors, a social scientist and a computer scientist, both at Cornell, require little background knowledge but include some more advanced mathematics in a number of end-of-chapter optional sections.
The seven major parts of three or four chapters each are Graph Theory and Social Networks, Game Theory, Markets and Strategic Interactions in Networks, Information Networks and the World Wide Web, Network Dynamics: Population Models, Network Dynamics: Structural Models, and Institutions and Aggregate Behavior. Each part is a mixture of background and applications. For example the Game Theory part includes chapters on Games, Evolutionary Game Theory, Modeling Network Traffic Using Game Theory, and Auctions. Each chapter in this and other parts includes interesting exercises at the level of a strong finite mathematics course.
The authors teach an introductory course using parts from each chapter. They suggest several other ways to use their text:
It would be very suitable as a motivating course for applied mathematics students who will understand some fascinating areas of growing importance as they learn the concepts needed to advance these fields.
This is a book that should be in every college library. Bright high-school students could start here too. It is a rare book that is neither trivial nor forbidding, with a rich wealth of material in areas that demand further exploration. Readers will no doubt find many ways to creatively incorporate these ideas into curricula or clubs and other activities at their institutions.
Art Gittleman (firstname.lastname@example.org) is Professor of Computer Science at California State University Long Beach.
1. Overview; Part I. Graph Theory and Social Networks: 2. Graphs; 3. Strong and weak ties; 4. Networks in their surrounding contexts; 5. Positive and negative relationships; Part II. Game Theory: 6. Games; 7. Evolutionary game theory; 8. Modeling network traffic using game theory; 9. Auctions; Part III. Markets and Strategic Interaction in Networks: 10. Matching markets; 11. Network models of markets with intermediaries; 12. Bargaining and power in networks; Part IV. Information Networks and the World Wide Web: 13. The structure of the Web; 14. Link analysis and Web search; 15. Sponsored search markets; Part V. Network Dynamics: Population Models: 16. Information cascades; 17. Network effects; 18. Power laws and rich-get-richer phenomena; Part VI. Network Dynamics: Structural Models: 19. Cascading behavior in networks; 20. The small-world phenomenon; 21. Epidemics; Part VII. Institutions and Aggregate Behavior: 22. Markets and information; 23. Voting; 24. Property.