The book "Random Graphs and Complex Networks" by Remco van der Hofstad provides a comprehensive overview of random graph models and their applications to real-world networks. The first volume focuses on the theoretical foundations and basic models, while the second volume delves into more advanced topics. The introduction to the book highlights the importance of studying random graphs as models for real-world networks, which have exhibited properties such as small-world phenomena and scale-free degree distributions. The book covers probabilistic methods, branching processes, and the Erdős-Rényi random graph model, among others. It also discusses the phase transition in the Erdős-Rényi random graph and the behavior of other random graph models for complex networks. Key topics include: - **Probabilistic Methods**: Convergence of random variables, coupling, stochastic ordering, probabilistic bounds, and martingales. - **Branching Processes**: Survival versus extinction, family moments, random-walk perspective, supercritical and subcritical processes, and Poisson branching processes. - **Erdős-Rényi Random Graphs**: Phase transitions, critical behavior, connectivity thresholds, and degree sequences. - **Generalized Random Graphs**: Motivation, model introduction, degree structure, and asymptotic equivalence. - **Configuration Model**: Motivation, introduction, and related results. - ** Preferential Attachment Models**: Motivation, model introduction, degree sequences, and related models. The book aims to be self-contained, providing necessary preliminaries and detailed proofs for classical results. It also includes exercises to help readers deepen their understanding. The author emphasizes the multidisciplinary nature of random graph theory and its applications in various fields, including economics, biology, and computer science.The book "Random Graphs and Complex Networks" by Remco van der Hofstad provides a comprehensive overview of random graph models and their applications to real-world networks. The first volume focuses on the theoretical foundations and basic models, while the second volume delves into more advanced topics. The introduction to the book highlights the importance of studying random graphs as models for real-world networks, which have exhibited properties such as small-world phenomena and scale-free degree distributions. The book covers probabilistic methods, branching processes, and the Erdős-Rényi random graph model, among others. It also discusses the phase transition in the Erdős-Rényi random graph and the behavior of other random graph models for complex networks. Key topics include: - **Probabilistic Methods**: Convergence of random variables, coupling, stochastic ordering, probabilistic bounds, and martingales. - **Branching Processes**: Survival versus extinction, family moments, random-walk perspective, supercritical and subcritical processes, and Poisson branching processes. - **Erdős-Rényi Random Graphs**: Phase transitions, critical behavior, connectivity thresholds, and degree sequences. - **Generalized Random Graphs**: Motivation, model introduction, degree structure, and asymptotic equivalence. - **Configuration Model**: Motivation, introduction, and related results. - ** Preferential Attachment Models**: Motivation, model introduction, degree sequences, and related models. The book aims to be self-contained, providing necessary preliminaries and detailed proofs for classical results. It also includes exercises to help readers deepen their understanding. The author emphasizes the multidisciplinary nature of random graph theory and its applications in various fields, including economics, biology, and computer science.