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Informationen zum Autor Remco van der Hofstad is Full Professor of Probability at Eindhoven University of Technology. He received the 2003 Prix Henri Poincaré (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. Klappentext 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. Zusammenfassung The first book to cover local convergence, this text discusses the local and global structure of random graph models for complex networks. Featuring examples of real-world networks for motivation and numerous exercises to build experience, it will be the definitive resource on the subject for researchers and graduate students. Inhaltsverzeichnis Preface; Possible course outline; Part I. Preliminaries: 1. Introduction and preliminaries; 2. Local convergence of random graphs; Part II. Connected Components in Random Graphs: 3. Connected components in general inhomogeneous random graphs; 4. Connected components in configuration models; 5. Connected components in preferential attachment models; Part III. Small-world Properties of Random Graphs: 6. Small-world phenomena in inhomogeneous random graphs; 7. Small-world phenomena in configuration models; 8. Small-world phenomena in preferential attachment models; Part IV. Related Models and Problems: 9. Related models; Appendix; Glossary; References; Index....
