Explore fundamental concepts of graph theory in this comprehensive lecture from CMU's "Great Ideas in Theoretical Computer Science" course. Delve into graph basics, including definitions, regular graphs, perfect matching, and connectivity. Learn about the World Wide Web's structure, register allocation in compilers, and key terminology in graph theory. Examine various graph properties, equivalence relations, and a crucial lemma. Gain insights into the pros and cons of different graph representations and other possibilities in this field. Enhance your understanding of theoretical computer science through this in-depth exploration of graphs led by Professor Ryan O'Donnell.