Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Conventions/Notations
- Part I Preliminaries
- Part II Erdős–Rényi–Gilbert Model
- 3 Uniform and Binomial Random Graphs
- 4 Evolution
- 5 Vertex Degrees
- 6 Connectivity
- 7 Small Subgraphs
- 8 Large Subgraphs
- 9 Extreme Characteristics
- Part III Modeling Complex Networks
- References
- Author Index
- Subject Index
3 - Uniform and Binomial Random Graphs
from Part II - Erdős–Rényi–Gilbert Model
Published online by Cambridge University Press: 02 March 2023
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Conventions/Notations
- Part I Preliminaries
- Part II Erdős–Rényi–Gilbert Model
- 3 Uniform and Binomial Random Graphs
- 4 Evolution
- 5 Vertex Degrees
- 6 Connectivity
- 7 Small Subgraphs
- 8 Large Subgraphs
- 9 Extreme Characteristics
- Part III Modeling Complex Networks
- References
- Author Index
- Subject Index
Summary
In this chapter, we formally introduce both Erdős–Rényi–Gilbert’s models, study their relationships, and establish conditions for their asymptotic equivalence. We also define and study the basic features of the asymptotic behavior of random graphs, i.e., the existence of thresholds for monotone graph properties.
Keywords
- Type
- Chapter
- Information
- Random Graphs and Networks: A First Course , pp. 29 - 44Publisher: Cambridge University PressPrint publication year: 2023