Spectral Graph Theory, Fall 2019
Not a lecture: Dan's favorite inequality
- Aug 28:
Introduction. Review of Graphs and Spectral Theory. Survey of highlights of the course.
Reading: Chapter 1 and Section 2.1. my notes
Files: 462Lect1.ipynb, 462Lect1.pdf,
- Aug 30: The Laplacian Matrix and Spectral Graph Drawing. Courant-Fischer.
Reading: Section 2.2 and Chapter 3. my notes.
- Sep 4: The Adjacency Matrix, interlacing, and Perron-Frobenius.
Reading: Chapter 4. my notes.
- Sep 9: Eigenvalues and Graph Structure: cuts, partitions, and coloring.
Reading: Chapter on "Independent Sets and Coloring" (but not Section 4) and Chapter on "Graph Partitioning". (now numbered 18 and 19). my notes.
- Sep 11: The Zoo of graphs. Bounding eigenvalues by test vectors.
Reading: Chapter 6. my notes.
- Sep 16: Eigenvalue comparison theorems.
Reading: Chapter 5. my notes. The Jupyter Notebook.
- Sep 18: Eigenvalues of random graphs.
Reading: Chapter 8. my notes. The Jupyter Notebook.
ps1 due, ps2 out.
- Sep 23: Partitioning in Stochastic Block Models.
Reading: Chapter 22. my notes. The Jupyter Notebook.
- Sep 25: Cheeger's inequality.
Reading: Chapter 21. my notes.
- Sep 30: Random Walks on Graphs
Reading: Chapter 10. my notes.
- Oct 2: Local graph clustering
ps2 due, ps3 out. my notes.
- Oct 7: Spring and resistor networks
Reading: Chapter 11. my notes.
- Oct 9: Elimination and Schur Complements. Effective Resistance.
Reading: Chapter 12. my notes.
- Oct 14: Spring embeddings of planar graphs.
Reading: Chapter 15. my notes.
- Oct 21: Computing Effective Resistance.
Reading: Chapter 14 and Section 12.3. my notes.
ps3 due, ps4 out.
- Oct 23: Introduction to Expander Graphs
Reading: Chapter 27. my notes.
- Oct 28: PSRGs via Random Walks on Expanders
Reading: Chapter 31, and maybe Section 4 of Chapter 7. my notes.
- Oct 30: Introduction to Coding Theory
Reading: Chapter 28. my notes.
- Nov 4: Expander Codes
Reading: Chapter 29. my notes.
ps4 due, ps5 out.
- Nov 6: A simple construction of expander graphs
Reading: Chapter 30. my notes.
- Nov 11: Sparsification of graphs by random sampling.
Reading: Chapter 32. my notes.
- Nov 13: Linear-sized sparsifiers of graphs.
Reading: Chapter 33. my notes.
- Nov 18: Iterative Solvers for Linear Equations.
Reading: Chapter 34. my notes.
ps5 due, ps6 out.
- Nov 20: The Conjugate Gradient
Reading: Chapter 35. my notes.
- Dec 2: Preconditioning by low-stretch spanning trees
Reading: Chapter 36. my notes.
- Dec 4: Nearly-linear time Laplacian solvers.
Reading: Chapter 37. my notes.