Random Graphs and Networks: A First Course

A rigorous yet accessible introduction to the rapidly expanding subject of random graphs and networks.

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

9781009260305, Cambridge University Press

Paperback / softback, published 9 March 2023

232 pages
24.4 x 17 x 1.2 cm, 0.381 kg

'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

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.

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.

Subject Areas: Computer science [UY], Discrete mathematics [PBD], Information theory [GPF]