Random Graphs and Complex Networks
Random Graphs and Complex Networks by Remco van der Hofstad, published by Cambridge University Press in 2017, offers a rigorous introduction to network science. This 321-page text presents random graphs as models for real-world networks, emphasizing their distinctive empirical properties. Designed for a master’s-level course, it is suitable for students with a basic background in probability and covers essential topics such as convergence of random variables, probabilistic bounds, and martingales.
Readers will find a systematic study of recent advances in the field, framed within a unified context. The book explores various models for complex networks, drawing on examples like the Internet and collaboration networks, while investigating key properties such as node connectivity. Numerous exercises are included to help students develop intuition and practical experience with the concepts presented, making this edition a valuable resource for those interested in the intersection of mathematics, algorithms, and networking.
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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.
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