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Introduction to Random Graphs

  • Date Published: October 2015
  • availability: Available
  • format: Hardback
  • isbn: 9781107118508


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About the Authors
  • 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
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    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

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    Product details

    • Date Published: October 2015
    • format: Hardback
    • isbn: 9781107118508
    • length: 478 pages
    • dimensions: 235 x 156 x 30 mm
    • weight: 0.81kg
    • contains: 25 b/w illus. 190 exercises
    • availability: Available
  • Table of Contents

    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
    Author index
    Main index.

  • 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.

    Michał Karoński, 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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