Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Introduction
- Part I Basic Setting
- Part II Probability Preliminaries
- Part III Network Models
- 11 The Bernoulli Random Graph
- 12 Models Related to the Bernoulli Random Graph
- 13 The Chung–Lu Model
- 14 The Configuration and GPDS Models
- 15 Random Geometric Graphs
- 16 Small World Graphs
- 17 Preferential Attachment Models
- 18 Dense Graph Limits and Graphon Models
- 19 Random Processes on Networks
- 20 Summary of Chapters 5–19
- Part IV Network Inference
- Appendix
- References
- Author Index
- Subject Index
17 - Preferential Attachment Models
from Part III - Network Models
Published online by Cambridge University Press: 11 June 2026
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Introduction
- Part I Basic Setting
- Part II Probability Preliminaries
- Part III Network Models
- 11 The Bernoulli Random Graph
- 12 Models Related to the Bernoulli Random Graph
- 13 The Chung–Lu Model
- 14 The Configuration and GPDS Models
- 15 Random Geometric Graphs
- 16 Small World Graphs
- 17 Preferential Attachment Models
- 18 Dense Graph Limits and Graphon Models
- 19 Random Processes on Networks
- 20 Summary of Chapters 5–19
- Part IV Network Inference
- Appendix
- References
- Author Index
- Subject Index
Summary
Preferential attachment models yield graphs that are generated as the result of a growth mechanism. Whenever a vertex is added to the graph, it is joined by edges to a number of the vertices already present in the graph, and these vertices are chosen with reference to their current popularity, as measured by their current degree. Models reflecting this general principle can be formulated in many different ways, some of which are discussed in the chapter. A useful property, observed when popularity is a linear function of degree, is that the degree distribution exhibits a power law decay in the tails, as the number of vertices in the graph increases. Other possible scenarios are also briefly discussed.
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- Chapter
- Information
- NetworksProbability and Statistics, pp. 543 - 559Publisher: Cambridge University PressPrint publication year: 2026
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