Random Graphs and Networks: A First Course

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.

‘Random Graphs and Networks: A First Course’ is a wonderful textbook that covers a remarkable set of topics written by two leading experts in the field. The textbook is comprehensive and contains a wealth of theoretical preliminaries, exercises and problems, making it ideal for an introductory course or for self-study. It is the best starting point in the present textbook market for any university student interested in the foundations of network science.’

Charalampos E. Tsourakakis - Boston University

'This is a very concise, highly informative introduction to the theory of random graphs and networks ... Essential.'

M. Bona Source: Choice

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Random Graphs and Networks: A First Course

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Contents

Frontmatter
pp i-iv

Dedication
pp v-vi

Contents
pp vii-viii

Preface
pp ix-ix

Acknowledgments
pp x-x

Conventions/Notations
pp xi-xiv

Part I - Preliminaries
pp 1-2

1 - Introduction
pp 3-7

2 - Basic Tools
pp 8-26

Part II - Erdős–Rényi–Gilbert Model
pp 27-28

3 - Uniform and Binomial Random Graphs
pp 29-44

4 - Evolution
pp 45-63

5 - Vertex Degrees
pp 64-77

6 - Connectivity
pp 78-84

7 - Small Subgraphs
pp 85-92

8 - Large Subgraphs
pp 93-110

9 - Extreme Characteristics
pp 111-124

Part III - Modeling Complex Networks
pp 125-126

10 - Inhomogeneous Graphs
pp 127-153

11 - Small World
pp 154-162

12 - Network Processes
pp 163-177

13 - Intersection Graphs
pp 178-196

14 - Weighted Graphs
pp 197-209

References
pp 210-215

Author Index
pp 216-217

Subject Index
pp 218-218

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Random Graphs and Networks: A First Course

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