Introduction to Random Graphs
£60.99
- Authors:
- Alan Frieze, Carnegie Mellon University, Pennsylvania
- Michał Karoński, Uniwersytet im. Adama Mickiewicza w Poznaniu, Poland
- Date Published: October 2015
- availability: Available
- format: Hardback
- isbn: 9781107118508
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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.
Read more- 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
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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
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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