Networks

Probability and Statistics
Erscheinungsjahr 2026
ISBN: 978-1-009-65172-1
Verlag: Cambridge University Press

Buch, Englisch, Band 57, 964 Seiten, Gewicht: 500 g

Reihe: Cambridge Series in Statistical and Probabilistic Mathematics

From social networks to biological systems, networks are a fundamental part of modern life. Network analysis is increasingly popular across the mathematical, physical, life and social sciences, offering insights into a range of phenomena, from developing new drugs based on intracellular interactions, to understanding the influence of social interactions on behaviour patterns. This book provides a toolkit for analyzing random networks, together with theoretical justification of the methods proposed. It combines methods from both probability and statistics, teaching how to build and analyze plausible models for random networks, and how to validate such models, to detect unusual features in the data, and to make predictions. Theoretical results are motivated by applications across a range of fields, and classical data sets are used for illustration throughout the book. This book offers a comprehensive introduction to the field for graduate students and researchers.

Autoren/Hrsg.

Barbour, A. D.

Reinert, Gesine

Inhaltsverzeichnis

1. Introduction; Part I. Basic Setting: 2. Network data sets; 3. Network summaries; 4. Models for networks; Part II. Probability Preliminaries: 5. Branching processes; 6. Some birth and death processes; 7. Poisson approximation; 8. Ramifications of Poisson approximation; 9. Normal approximation; 10. Multivariate normal approximation; 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: 21. Sampling from networks; 22. Estimation: fitting a network model; 23. Assessing model fit; 24. Community detection; 25. Using networks for inference; 26. Some further topics; Appendix; References; Index.

Über Autor(innen)

Barbour, A. D.
A. D. Barbour is Emeritus Professor of Mathematics at the University of Zürich. He is also Honorary Professorial Fellow in Mathematics at the University of Melbourne and Fellow of the Institute of Mathematical Statistics. He previously co-authored the monographs 'Poisson Approximation' (1992) and 'Logarithmic Combinatorial Structures: A Probabilistic Approach' (2003).

Reinert, Gesine
Gesine Reinert is Professor of Statistics and Fellow of Keble College at the University of Oxford. She is also Fellow of the Institute of Mathematical Statistics. Her research spans applied probability, network science, computational biology, and theoretical foundations of machine learning.