Networks
Probability and Statistics
Will be published approx. on 25. June 2026
Book
Hardback
964 pages
978-1-009-65172-1 (ISBN)
Description
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.
Reviews / Votes
'An unusual blend of practical examples, probabilistic treatment of important random graph models, description and analysis of statistical methods, all written with clarity, insight, and competence. A wonderful addition to the current literature!' Steffen Lauritzen, Emeritus Professor of Statistics, Oxford University and University of Copenhagen 'Barbour and Reinert's Networks: Probability and Statistics provides a rigorous and insightful guide to the theory, applications, and further development of network science. Essential reading for anyone seeking to understand and advance probabilistic and statistical methods for modern networks.' Chenlei Leng, University of Warwick 'The study of probability and statistics for network analysis has exploded over the past 20 years. And the tools for working in this area are varied, ranging from needing an understanding of how networks arise and their empirical properties to a facility with aspects of modern probability and statistics not usually encountered in introductory courses. This book does a lovely job of organizing and making accessible a substantial portion of the core probability models and statistical inference methods in this large, diverse and still rapidly evolving field. The layered approach - covering topics first at a higher level and then digging down more deeply - will be appreciated by both students and instructors alike. Detailed background chapters and appendices further make this book a resource for a wide audience as to not only what we know about networks from probabilistic and statistical perspectives but also how we know it.' Eric D. Kolaczyk, McGill UniversityMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Product notice
Laminated cover
Illustrations
Worked examples or Exercises
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 48 mm
Weight
500 gr
ISBN-13
978-1-009-65172-1 (9781009651721)
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Schweitzer Classification
Persons
A. D. Barbour is Emeritus Professor of Mathematics at the University of Zuerich. 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). 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.
Content
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.