Networks

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). 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.

• 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.

'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