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.
|Publisher:||Cambridge University Press|
|Series:||Cambridge Series in Statistical and Probabilistic Mathematics Series , #43|
|Product dimensions:||6.97(w) x 9.96(h) x (d)|
About the Author
Remco van der Hofstad is Full Professor of Probability at Eindhoven University of Technology and Acting Scientific Director of the European Institute for Statistics, Probability, Stochastic Operations Research and their Applications (Eurandom). He has authored over 100 research articles and has taught courses on random graphs at over ten institutions. He received the 2003 Prix Henri Poincaré (jointly with Gordon Slade) and the 2007 Rollo Davidson Prize, and he is a laureate of the 2003 Innovative Research VIDI Scheme and the 2008 Innovative Research VICI Scheme.
Table of Contents
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.