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.

‘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 University