To try everything Brilliant has to offer—free—for a full 30 days, visit . You’ll also get 20% off an annual premium subscription. This video was sponsored by Brilliant. --- References: 1. Cornell University Lecture Note: 2. Spectral Graph Theory Lecture by Steve Butler: 3. Spectral Graph Theory Lecture by Radu Horaud: ~tom/Clustering/ 4. Tutorial by Daniel A. Spielman: 5. This Stack Exchange question: 6. And this Quora question: --- Timestamp: 0:00 Introduction 0:30 Outline 00:57 Review of Graph Definition and Degree Matrix 03:34 Adjacency Matrix Review 05:03 Review of Necessary Linear Algebra 09:09 Introduction of The Laplacian Matrix 15:36 Why is L called the Laplace Matrix 18:14 Eigenvalue 0 and Its Eigenvector 20:27 Fiedler Eigenvalue and Eigenvector 23:56 Sponsorship Message 25:02 Spectral Embedding 25:38 Spectral Embedding Application: Spectral Clustering 27:51 Outro ​ --- Big thanks to professor Fan Chung Graham and professor Robert Ellis for the email conversations.