Complex networks are key to describing the connected nature of the society that we live in. This book, the second of two volumes, describes the local structure of random graph models for real-world networks and determines when these models have a giant component and when they are small-, and ultra-small, worlds. This is the first book to cover the theory and implications of local convergence, a crucial technique in the analysis of sparse random graphs. Suitable as a resource for researchers and PhD-level courses, it uses examples of real-world networks, such as the Internet and citation networks, as motivation for the models that are discussed, and includes exercises at the end of each chapter to develop intuition. The book closes with an extensive discussion of related models and problems that demonstratemodern approaches to network theory, such as community structure and directed models.

About the Author

Remco van der Hofstad is Full Professor of Probability at Eindhoven University of Technology. He received the 2003 Prix Henri Poincar� (jointly with Gordon Slade) and the 2007 Rollo Davidson Prize, and he is a laureate of the 2003 Innovative Research VIDI Scheme and the 2008 Innovative Research VICI Scheme. He served as scientific director at Eurandom from 2011 to 2019, and is a member of the Dutch Royal Academy of Science. Van der Hofstad is one of the principal investigators of the prestigious NETWORKS Gravitation Program and is the creator of the interactive website networkpages.nl, aimed at a broad audience.

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