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Introduction to Random Graphs

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Introduction to Random Graphs

Introduction to Random Graphs

Alan Frieze , Carnegie Mellon University, Pennsylvania
Michał Karoński , Uniwersytet im. Adama Mickiewicza w Poznaniu, Poland
October 2015
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Hardback
9781107118508

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    Description

    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.

    • Brings the reader up to date with modern developments, including matchings in hypergraphs, containers and interpolation
    • Covers many basic tools that will be useful in all aspects of probabilistic combinatorics
    • Over 180 exercises test students' grasp of the material

    Reviews & endorsements

    'This is a well-planned book that is true to its title in that it is indeed accessible for anyone with just an undergraduate student's knowledge of enumerative combinatorics and probability.' Miklós Bóna, MAA Reviews

    See more reviews

    Product details

    October 2015
    Hardback
    9781107118508
    478 pages
    235 × 156 × 30 mm
    0.85kg
    25 b/w illus. 190 exercises
    Available

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    This title is available for institutional purchase via Cambridge Core

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    Contents

    Table of Contents

    • 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.
      • Show more

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    About the authors
      Authors
    • Alan Frieze , Carnegie Mellon University, Pennsylvania

      Alan Frieze is a Professor in the Department of Mathematical Sciences at Carnegie Mellon University, Pennsylvania. He has authored more than 300 publications in top journals and was invited to be a plenary speaker at the Seoul ICM 2014. In 1991 he received the Fulkerson prize in discrete mathematics.

    • MichaÅ‚ KaroÅ„ski , Uniwersytet im. Adama Mickiewicza w Poznaniu, Poland

      Michał Karoński is a founder of the Discrete Mathematics Research group at Adam Mickiewicz University in Poznan, Poland. He has authored over 50 publications and currently serves as co-Editor-in-Chief of Random Structures and Algorithms.

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