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  • Cited by 24
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Baroni, Enrico van der Hofstad, Remco and Komjáthy, Júlia 2019. Tight Fluctuations of Weight-Distances in Random Graphs with Infinite-Variance Degrees. Journal of Statistical Physics,

    van der Hofstad, Remco van Leeuwaarden, Johan S. H. and Stegehuis, Clara 2018. Triadic Closure in Configuration Models with Unbounded Degree Fluctuations. Journal of Statistical Physics, Vol. 173, Issue. 3-4, p. 746.

    Martin, James B. and Yeo, Dominic 2018. Critical random forests . Latin American Journal of Probability and Mathematical Statistics, Vol. 15, Issue. 2, p. 913.

    Wang, Tiandong and Resnick, Sidney I. 2018. Consistency of Hill estimators in a linear preferential attachment model. Extremes,

    Dereich, Steffen and Ortgiese, Marcel 2018. Local Neighbourhoods for First-Passage Percolation on the Configuration Model. Journal of Statistical Physics, Vol. 173, Issue. 3-4, p. 485.

    Garavaglia, A. and van der Hofstad, R. 2018. From trees to graphs: collapsing continuous-time branching processes. Journal of Applied Probability, Vol. 55, Issue. 3, p. 900.

    Janson, Svante 2018. On Edge Exchangeable Random Graphs. Journal of Statistical Physics, Vol. 173, Issue. 3-4, p. 448.

    Polito, Federico 2018. Studies on generalized Yule models. Modern Stochastics: Theory and Applications, p. 1.

    Bhamidi, Shankar van der Hofstad, Remco and Sen, Sanchayan 2018. The multiplicative coalescent, inhomogeneous continuum random trees, and new universality classes for critical random graphs. Probability Theory and Related Fields, Vol. 170, Issue. 1-2, p. 387.

    Liu, Qun and Dong, Zhi Shan 2018. Large Deviations in Generalized Random Graphs with Node Weights. Acta Mathematica Sinica, English Series, Vol. 34, Issue. 10, p. 1626.

    Kang, Mihyun Pachon, Angelica and Rodríguez, Pablo M. 2018. Evolution of a Modified Binomial Random Graph by Agglomeration. Journal of Statistical Physics, Vol. 170, Issue. 3, p. 509.

    Minati, Gianfranco and Pessa, Eliano 2018. From Collective Beings to Quasi-Systems. p. 287.

    Dommers, Sander Giardinà, Cristian Giberti, Claudio and Hofstad, Remco van der 2018. Large Deviations for the Annealed Ising Model on Inhomogeneous Random Graphs: Spins and Degrees. Journal of Statistical Physics, Vol. 173, Issue. 3-4, p. 1045.

    Medvedev, Alexey and Pete, Gábor 2018. Speeding up non-Markovian first-passage percolation with a few extra edges. Advances in Applied Probability, Vol. 50, Issue. 3, p. 858.

    Rockmore, Daniel N. Fang, Chen Foti, Nicholas J. Ginsburg, Tom and Krakauer, David C. 2018. The cultural evolution of national constitutions. Journal of the Association for Information Science and Technology, Vol. 69, Issue. 3, p. 483.

    Bannink, Tom van der Hofstad, Remco and Stegehuis, Clara 2018. Switch chain mixing times and triangle counts in simple random graphs with given degrees. Journal of Complex Networks,

    Garlaschelli, Diego den Hollander, Frank and Roccaverde, Andrea 2018. Covariance Structure Behind Breaking of Ensemble Equivalence in Random Graphs. Journal of Statistical Physics, Vol. 173, Issue. 3-4, p. 644.

    Deijfen, Maria Rosengren, Sebastian and Trapman, Pieter 2018. The Tail does not Determine the Size of the Giant. Journal of Statistical Physics, Vol. 173, Issue. 3-4, p. 736.

    Cardinaels, Ellen van Leeuwaarden, Johan S. H. and Stegehuis, Clara 2018. Algorithms and Models for the Web Graph. Vol. 10836, Issue. , p. 1.

    Gel, Yulia R. Lyubchich, Vyacheslav and Ramirez Ramirez, L. Leticia 2017. Bootstrap quantification of estimation uncertainties in network degree distributions. Scientific Reports, Vol. 7, Issue. 1,

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Book description

This rigorous introduction to network science presents random graphs as models for real-world networks. Such networks have distinctive empirical properties and a wealth of new models have emerged to capture them. Classroom tested for over ten years, this text places recent advances in a unified framework to enable systematic study. Designed for a master's-level course, where students may only have a basic background in probability, the text covers such important preliminaries as convergence of random variables, probabilistic bounds, coupling, martingales, and branching processes. Building on this base - and motivated by many examples of real-world networks, including the Internet, collaboration networks, and the World Wide Web - it focuses on several important models for complex networks and investigates key properties, such as the connectivity of nodes. Numerous exercises allow students to develop intuition and experience in working with the models.

Reviews

‘… a modern and deep, yet accessible, introduction to the models that make up [the] basis for the theoretical study of random graphs and complex networks. The book strikes a balance between providing broad perspective and analytic rigor that is a pleasure for the reader.’

Adam Wierman - California Institute of Technology

‘This text builds a bridge between the mathematical world of random graphs and the real world of complex networks. It combines techniques from probability theory and combinatorics to analyze the structural properties of large random graphs. Accessible to network researchers from different disciplines, as well as masters and graduate students, the material is suitable for a one-semester course, and is laced with exercises that help the reader grasp the content. The exposition focuses on a number of core models that have driven recent progress in the field, including the Erdős–Rényi random graph, the configuration model, and preferential attachment models. A detailed description is given of all their key properties. This is supplemented with insightful remarks about properties of related models so that a full panorama unfolds. As the presentation develops, the link to complex networks provides constant motivation for the routes that are being chosen.’

Frank den Hollander - Leiden University

‘The first volume of Remco van der Hofstad's Random Graphs and Complex Networks is the definitive introduction into the mathematical world of random networks. Written for students with only a modest background in probability theory, it provides plenty of motivation for the topic and introduces the essential tools of probability at a gentle pace. It covers the modern theory of Erdős–Rényi graphs, as well as the most important models of scale-free networks that have emerged in the last fifteen years. This is a truly wonderful first volume; the second volume, leading up to current research topics, is eagerly awaited.’

Peter Mörters - University of Bath

‘This new book on random graph models for complex networks is a wonderful addition to the field. It takes the uninitiated reader from the basics of graduate probability to the classical Erdős–Rényi random graph before terminating at some of the fundamental new models in the discipline. The author does an exemplary job of both motivating the models of interest and building all the necessary mathematical tools required to give a rigorous treatment of these models. Each chapter is complemented by a comprehensive set of exercises allowing the reader ample scope to actively master the techniques covered in the chapter.’

Shankar Bhamidi - University of North Carolina, Chapel Hill

‘This book is invaluable for anybody who wants to learn or teach the modern theory of random graphs and complex networks. I have used it as a textbook for long and short courses at different levels. Students always like the book because it has all they need: exciting high-level ideas, motivating examples, very clear proofs, and an excellent set of exercises. Easy to read, extremely well structured, and self-contained, the book builds proficiency with random graph models essential for state-of-the-art research.’

Nelly Litvak - University of Twente

'What makes the book particularly interesting is that it provides all important preliminaries for readers not having the basic background knowledge of random graphs. … The book is well-suited for a graduate course on random graphs, where students may only have minimal background in probability theory, as the book provides plenty of motivation for the topic and covers all important preliminaries. All the chapters are supplemented by extensive exercises to develop better intuition and to progressively master the models covered in the book. In a nutshell, the book is easy to follow and well-organized for developing proficiency in random graph models necessary for state of the art research.'

Ghulam Abbas Source: Complex Adaptive Systems Modeling

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