Random Graphs and Complex Networks

This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.

Remco van der Hofstad (Author)

9781107172876, Cambridge University Press

Hardback, published 22 December 2016

236 pages, 58 b/w illus. 5 tables
26.2 x 18.4 x 2.2 cm, 0.79 kg

'The writing is of a high standard. I would certainly recommend it to a starting graduate student, even if their first degree was not mathematics.' Tobias Muller, Nieuw Archief voor Weskunde

This rigorous introduction to network science presents random graphs as models for real-world networks. Such networks have distinctive empirical properties and a wealth of new models have emerged to capture them. Classroom tested for over ten years, this text places recent advances in a unified framework to enable systematic study. Designed for a master's-level course, where students may only have a basic background in probability, the text covers such important preliminaries as convergence of random variables, probabilistic bounds, coupling, martingales, and branching processes. Building on this base - and motivated by many examples of real-world networks, including the Internet, collaboration networks, and the World Wide Web - it focuses on several important models for complex networks and investigates key properties, such as the connectivity of nodes. Numerous exercises allow students to develop intuition and experience in working with the models.

Preface
Course outline
1. Introduction
Part I. Preliminaries: 2. Probabilistics methods
3. Branching processes
Part II. Basic Models: 4. Phase transition for the Erdos–Renyi random graph
5. Erdos–Renyi random graph revisited
Part III. Models for Complex Networks: 6. Generalized random graphs
7. Configuration model
8. Preferential attachment models
Appendix
Glossary
References
Index.

Subject Areas: Network management [UTF], Algorithms & data structures [UMB], Stochastics [PBWL], Probability & statistics [PBT]