Introduction to random graphs

著者

書誌事項

Introduction to random graphs

Alan Frieze, Michał Karoński

Cambridge University Press, 2016

  • : hardback

大学図書館所蔵 件 / 全9件

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注記

Includes bibliographical references and index

内容説明・目次

内容説明

From social networks such as Facebook, the World Wide Web and the Internet, to the complex interactions between proteins in the cells of our bodies, we constantly face the challenge of understanding the structure and development of networks. The theory of random graphs provides a framework for this understanding, and in this book the authors give a gentle introduction to the basic tools for understanding and applying the theory. Part I includes sufficient material, including exercises, for a one semester course at the advanced undergraduate or beginning graduate level. The reader is then well prepared for the more advanced topics in Parts II and III. A final part provides a quick introduction to the background material needed. All those interested in discrete mathematics, computer science or applied probability and their applications will find this an ideal introduction to the subject.

目次

  • Preface
  • Part I. Basic Models: 1. Random graphs
  • 2. Evolution
  • 3. Vertex degrees
  • 4. Connectivity
  • 5. Small subgraphs
  • 6. Spanning subgraphs
  • 7. Extreme characteristics
  • 8. Extremal properties
  • Part II. Basic Model Extensions: 9. Inhomogeneous graphs
  • 10. Fixed degree sequence
  • 11. Intersection graphs
  • 12. Digraphs
  • 13. Hypergraphs
  • Part III. Other Models: 14. Trees
  • 15. Mappings
  • 16. k-out
  • 17. Real-world networks
  • 18. Weighted graphs
  • 19. Brief notes on uncovered topics
  • Part IV. Tools and Methods: 20. Moments
  • 21. Inequalities
  • 22. Differential equations method
  • 23. Branching processes
  • 24. Entropy
  • References
  • Author index
  • Main index.

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