Random Graphs and Networks: A First Course

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Alan Frieze (Carnegie Mellon University, Pennsylvania) Michał Karoński (Adam Mickiewicz University, Poznań, Poland)

Random Graphs and Networks

A First Course

Alan Frieze (Carnegie Mellon University, Pennsylvania), Michał Karoński (Adam Mickiewicz University, Poznań, Poland)

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English

Cambridge University Press
09 March 2023

Information theory; Discrete mathematics; Computer science

Networks surround us, from social networks to protein–protein interaction networks within the cells of our bodies. The theory of random graphs provides a necessary framework for understanding their structure and development. This text provides an accessible introduction to this rapidly expanding subject. It covers all the basic features of random graphs – component structure, matchings and Hamilton cycles, connectivity and chromatic number – before discussing models of real-world networks, including intersection graphs, preferential attachment graphs and small-world models.

Based on the authors' own teaching experience, it can be used as a textbook for a one-semester course on random graphs and networks at advanced undergraduate or graduate level. The text includes numerous exercises, with a particular focus on developing students' skills in asymptotic analysis. More challenging problems are accompanied by hints or suggestions for further reading.

By: Alan Frieze (Carnegie Mellon University Pennsylvania), Michał Karoński (Adam Mickiewicz University, Poznań, Poland)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 244mm, Width: 170mm, Spine: 12mm
Weight: 381g
ISBN: 9781009260305
ISBN 10: 1009260308
Pages: 232
Publication Date: 09 March 2023
Audience: General/trade , ELT Advanced
Format: Paperback
Publisher's Status: Active

Conventions/Notation; Part I. Preliminaries: 1. Introduction; 2. Basic tools; Part II. Erdos–Rényi–Gilbert Model: 3. Uniform and binomial random graphs; 4. Evolution; 5. Vertex degrees; 6. Connectivity; 7. Small subgraphs; 8. Large subgraphs; 9. Extreme characteristics; Part III. Modeling Complex Networks: 10. Inhomogeneous graphs; 11. Small world; 12. Network processes; 13. Intersection graphs; 14. Weighted graphs; References; Author index; Main index.

Alan Frieze is Professor in the Department of Mathematical Sciences at Carnegie Mellon University. He has authored almost 400 publications in top journals and was a plenary speaker at the 2014 International Congress of Mathematicians. Michał Karoński is Professor Emeritus in the Faculty of Mathematics and Computer Science at Adam Mickiewicz University, where he founded the Discrete Mathematics group. He served as Editor-in-Chief of 'Random Structures and Algorithms' for thirty years.

Reviews for Random Graphs and Networks: A First Course

'Random Graphs and Networks: A First Course' is a wonderful textbook that covers a remarkable set of topics written by two leading experts in the field. The textbook is comprehensive and contains a wealth of theoretical preliminaries, exercises and problems, making it ideal for an introductory course or for self-study. It is the best starting point in the present textbook market for any university student interested in the foundations of network science.' Charalampos E. Tsourakakis, Boston University