Introduction to Random Graphs

by Alan Frieze, Michal Karonski

Overview

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.

Product Details

ISBN-13:	9781107118508
Publisher:	Cambridge University Press
Publication date:	10/26/2015
Edition description:	New Edition
Pages:	478
Product dimensions:	6.14(w) x 9.25(h) x 1.18(d)

About the Author

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 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.

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.

Editorial Reviews

"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 the Publisher