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Introduction to random graphs

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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  Read more...

Abstract:
This book covers random graphs from the basic to the advanced and will appeal to anyone interested in combinatorics, applied probability or theoretical computer science. Having read this book, the  Read more...

Author(s): Frieze, Alan M.; Karoński, Michał
Edition: draft
Publisher: Cambridge University Press
Year: 2016

Language: English
Pages: 464
City: Cambridge
Tags: Random graphs.;Combinatorial probabilities.;Probabilities.;Graphes aléatoires.;Probabilités combinatoires.;Graphes aléatoires.;Probabilités combinatoires.;Probabilités.

Content: 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.