ランダム・グラフと複雑ネットワーク Random Graphs and Complex Networks (Cambridge Series in Statistical and Probabilistic Mathematics)

Hofstad, Remco van der

Cambridge University Press（2016/12発売）

• 製本 Hardcover:ハードカバー版／ページ数 236 p.
• 言語 ENG
• 商品コード 9781107172876
• DDC分類 511.5

Full Description

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.

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.