Introduction to Random Graphs

The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.

Alan Frieze (Author), Micha? Karo?ski (Author)

9781107118508, Cambridge University Press

Hardback, published 26 October 2015

478 pages, 25 b/w illus. 190 exercises
23.5 x 15.6 x 3 cm, 0.81 kg

'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

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.

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.

Subject Areas: Combinatorics & graph theory [PBV], Algebra [PBF], Discrete mathematics [PBD], Mathematics [PB]