Spectral Graph Theory - Minimizing/Maximizing the Quadratic Form

Explore spectral graph theory in this graduate-level lecture from Carnegie Mellon University's "CS Theory Toolkit" course. Delve into the intricacies of minimizing and maximizing a graph's quadratic form, subject to normalization constraints. Examine the connections between these concepts and graph properties such as connected components and bipartiteness. Learn from Professor Ryan O'Donnell as he guides you through key topics including scaling considerations, natural scaling, and intuition for maximizing the quadratic form. Gain valuable insights from Spielman's "Spectral and Algebraic Graph Theory" book, which serves as a resource for this 33-minute lecture. Enhance your understanding of fundamental concepts in theoretical computer science and prepare for advanced research in the field.

Introduction
How small can the quadratic form be
Scaling considerations
Natural scaling
Intuition for maximizing quadratic form
Proof
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