Random Graphs and Networks

A First Course
Erscheinungsjahr 2023
ISBN: 978-1-009-26028-2
Verlag: Cambridge University Press

Buch, Englisch, 232 Seiten, Format (B × H): 170 mm x 244 mm, Gewicht: 572 g

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.

Autoren/Hrsg.

Frieze, Alan

Karo&

Karonski, Michal

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Informationstheorie, Kodierungstheorie
• Mathematik | Informatik EDV | Informatik Informatik
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik

Inhaltsverzeichnis

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.

Über Autor(innen)

Karonski, Michal
Michal Karonski 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.

Frieze, Alan
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.