Random graphs and complex networks
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 …
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- Full title :Random graphs and complex networks. / Remco van der Hofstad, Technische Universiteit Eindhoven.
Summary
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.
Read More ↓Edition Statements
- Publication Date:2017.
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge
- Language:eng
- Publication Date:2017.
Notes
Title from publisher's bibliographic system (viewed on 31 Jan 2017).
The Physical Object
- Description:1 online resource (xvi, 321 pages)
Edition Identifiers
- ISBN:9781316779422, 1316779424
- oclc:ocn976446103
- LC Classification:QA166.17
- Dewey Decimal:511/.5
Table of Contents
Cover -- Half-title page -- Series page -- Title page -- Copyright page -- Dedication page -- Contents -- Preface -- Course Outline -- 1 Introduction -- 1.1 Motivation -- 1.2 Graphs and Their Degree and Connectivity Structure -- 1.3 Complex Networks: the Infamous Internet Example -- 1.4 Scale-Free, Highly Connected and Small-World Graph Sequences -- 1.5 Further Network Statistics -- 1.6 Other Real-World Network Examples -- 1.7 Tales of Tails -- 1.8 Random Graph Models for Complex Networks -- 1.9 Notation -- 1.10 Notes and Discussion -- 1.11 Exercises for Chapter 1 -- Part I Preliminaries -- 2 Probabilistic Methods -- 2.1 Convergence of Random Variables -- 2.2 Coupling -- 2.3 Stochastic Ordering -- 2.4 Probabilistic Bounds -- 2.5 Martingales -- 2.6 Order Statistics and Extreme Value Theory -- 2.7 Notes and Discussion -- 2.8 Exercises for Chapter 2 -- 3 Branching Processes -- 3.1 Survival versus Extinction -- 3.2 Family Moments -- 3.3 Random-Walk Perspective to Branching Processes -- 3.4 Supercritical Branching Processes -- 3.5 Hitting-Time Theorem and the Total Progeny -- 3.6 Properties of Poisson Branching Processes -- 3.7 Binomial and Poisson Branching Processes -- 3.8 Notes and …
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