Meysam Miralaei
Summary: Random graphs, first studied by Erdős and Rényi, provide a powerful framework for analyzing complex structures in mathematics, computer science, and real-world networks. This course introduces fundamental models such as G(n,p), random regular graphs, and the configuration model, emphasizing threshold phenomena, extremal properties, and expansion. It also explores modern extensions that capture features of real networks, including preferential attachment, Watts–Strogatz, and Chung–Lu models. The material balances accessibility with depth, offering both a foundation in probabilistic methods and connections to current research directions.