CHAPTER 1 Eigenvalues and the Laplacian of a graph 1.1. Aug. 29: Introduction and course overview. T-Th 2:30-3:45 in AKW 500 hypercubes, and random graphs. in Computational and Applied Mathematics and a B.S. Expander graphs, some of their applications, and connections to error-correcting codes. preferences. Spectral Graph Theory and its Applications Applied Mathematics 500A . Due to the recent discovery of very fast solvers for these equations, they are also becoming increasingly useful in combinatorial opti- course on Spectral Graph Theory. Spectral graph theory is the study and exploration of graphs through the eigenvalues and eigenvectors of matrices naturally associated with those graphs. It is intuitively related to attempts to understand graphs through the simulation of processes on graphs and through the consideration of physical systems related to graphs. Sterling Professor of Computer Science and Professor of Statistics & Data Science and of Mathematics This book is mostly based on lecture notes from the \Spectral Graph Theory" course that I have taught at Yale, with notes from \Graphs and Networks" and \Spectral Graph Theory and its Applications" mixed in. CPSC 662 / AMTH 561: Spectral Graph Theory. At Yale, this probably means Math 244 or CPSC 365, and at least one of Math 230/231, 300 or 301. tral graph theory, Spielman and Teng34 introduced a notion of spectral similarity for two graphs. of Computer Science Program in Applied Mathematics Yale Unviersity This version of the course will assume less familiarity with a mathematics curriculum. Applications to optimization, numerical linear algebra, error-correcting codes, computational biology, and the discovery of graph structure. Dan Spielman. Preconditioning by augmented trees (11/11/04), Lecture 20. Solving Linear Systems (11/9/04), Lecture 19. We will first describe it as a generalization of cut similarity. path graphs. Diameter, Doubling, and Applications, Lecture 18. Given a weighted graph = (, V w), we define the G Laplacian quadratic form of to be the function G Q G from RV to R given by If S is a set of vertices and x is the characteristic vector of S Graphs and Networks V: a set of vertices (nodes) E: a set of edges an edge is a pair of vertices Dan Study Log. Topics: Cutting graphs and Cheeger's inequality. Yale University AMS Josiah Willard Gibbs Lecture January 6, 2016 . So, they may contain mistakes and strange grammar. AMTH 561/CPSC 662, is a graduate course on Spectral Graph Theory and related topics. CPSC 462/562 is the latest incarnation of my course matrices. Jay is currently pursing a postdoctoral fellowship at Yale University. A Social Network Graph . Tutte's rubber band embeddings of planar graphs (11/30/04). Fall 2018. Introduction Spectral graph theory has a long history. As a methodological approach, SNA refers to a catalog of techniques steeped in mathematical graph theory and now extending to statistical simulation and algebraic models. It will also include some related content that is not strictly linear algebraic, and some that does not have much to do with graphs, but which I include because it is worth knowing. Suggested topics for future lectures, please provide In the early days, matrix theory and linear algebra were used to â¦ Related Jupyter notebooks will appear on this page later. â INTRODUCTIONâ Spectral graph theory starts by associating matrices to graphs, notably, the adja- cency matrix and the laplacian matrix. The construction of a diffusion process on the graph is a classical topic in spectral graph theory [weighted graph Lapla-cian normalization (8)], and the procedure consists in renor-malizing the kernel k(x, y) as follows: for all x X, let v x X k x, y d y, and set a x, y k x, y v ix. AMTH 500, Spectral Graph Theory & Apps: An applied approach to spectral graph theory. From the first lecture in 2009, â this course is about the eigenvalues and eigenvectors of matrices associated with graphs, and their applications. Course website. You could also think of this as a course in "how to talk with Dan", because Schur complements, effective resistance and some of their applications. Note: These plans may change, and I have not yet decided on the content of the last 4 lectures. of Computer Science Program in Applied Mathematics Yale Unviersity. Readings for the course will come from drafts of a book that I am writing, and which I will post on this page. One warning about the lecture notes is in order: I write them in one Spectral Graph Theory, Fall 2015 Applied Mathematics 561/ Computer Science 662 . 8/1/09-7/31/12. Spectral Graph Matching Event time: Friday, October 4, 2019 - 11:00am. The combinatorial meaning of the eigenvalues and eigenvectors of matrices associated with graphs. The general theme is then, ï¬rstly, to compute or estimate the eigenvalues of such matrices, and secondly, to relate the eigenval- ues to structural properties of graphs. 2 Spectral Graph Theory The basic premise of spectral graph theory is that we can study graphs by considering their matrix representations. Jupyter Notebook, and an HTML version of that, and files used in the lecture: dodec.txt; YALE.jld2 The less obvious requirements are "mathematical maturity" and "mathematical literacy". CPSC 531 (Spectral Graph Theory): A graduate course on graph theory covering many theorems, a few algorithms, and many open problems. CPSC 662 Spectral Graph Theory Daniel Spielman: MW 2.30-3.45 at WTS A60 : S&DS 600 Advanced Probability Sekhar Tatikonda: TT 2:30-3:45 at ML 211 : CPSC 659 Building Interactive Machines Marynel Vazquez: MW 1.00-2.15 at AKW 200 : CPSC 575 Computational Vision and Biological Perception My Fall 2016 course on algorithmic spectral graph theory. One warning about the lecture notes is in order: I write them in one draft, without looking back. daniel.spielman@yale.edu Phone: 203-436-1264 Website Research Interests: Analysis of algorithms and heuristics, error-correcting codes, combinatorial scientific computing, spectral graph theory, and combinatorics. I hope that it will provide a convenient reference for both the course and for lots of exciting material that we will not have time to cover. Spielman, Daniel. Instructor: Dan Spielman. At Yale, Jay is working on his PhD in Computational Biology and Bioinformatics. Connections to Spring and Electrical networks. The course description may be found here. I find that almost every research question I address somehow relates Event description: Theory Seminar. COMPSCI 638: Graph Algorithms October 23, 2019 Lecture 17 Lecturer: Debmalya Panigrahi Scribe: Kevin Sun 1 Overview In this lecture, we look at the fundamental concepts of spectral graph theory. Graph partitioning and Cheeger's inequality. It will be taught in the style of a math class. Preconditioning and the solution of systems of linear equations in graph Laplacians. Graph Decomposotions (11/18/04), Lecture 21. An introduction to the "animals in the Zoo": the spectra of some fundamental graphs: paths, trees, rings, grids, back to material covered in this course. Lecture 8. Analysis of random walks on graphs, and Poincare inequalities. Lap Chi Lau, University of Waterloo Fall 2015. His research interests are Spectral Graph Theory, Signal Processing, Dimensionality reduction, data visualization. Yale University Toronto, Sep. 28, 2011 . I love the material in these courses, and nd that I can â¦ The obvious prerequisites for this course are knowledge of linear algebra and exposure to graph theory. Luca Trevisan, UC Berkeley Stanford course, Winter 2011. You can find the schedule of lectures and assignments, here. Christopher is interested in spectral graph theory, combinatorial optimization, and applications to machine learning. their Laplacians. You could think of this as a course in "Advanced Linear Algebra Student and faculty explanations of current research in areas such as random graph theory, spectral graph theory, Markov chains on graphs, and the objective method. Topics: Lower bounding \lambda_2, and draft, without looking back. Most lectures will cover some essential element of Linear Algebra or Nisheeth Vishnoi, EPFL, Lx = b. Chris Godsil and Gordon Royle, Algebraic Graph Theory. Time: M-W 2:30-3:45. Dan Spielman, Yale University, Fall 2015. Spectral and Electrical Graph Theory Daniel A. Spielman Dept. He earned a B.A. Available in. Christopher Harshaw is a Ph.D. student advised by Professors Daniel Spielman and Amin Karbasi. I have chosen to only present material that I consider beautiful. YALE 2004 WORKSHOP on DISCRETE MATHEMATICS and THEORETICAL COMPUTER SCIENCE, Concentration of eigenvalues of random Whereas the previous versions, numbered AMTH 561 and CPSC 662, were essentially taught as graduate mathematics courses, this version is suitable for undergraduates and has a more applied focus. Sekhar Tatikonda NSF CCF-0915487: \Spectral Graph Theory, Point Clouds, and Linear Equation Solvers\. Textbooks include: I Spectral and Algebraic Graph Theory (Daniel A. Spielman) I Scalable Algorithms for Data and Network Analysis (Shang-Hua Teng) About the Course 5 Objective of the course: I To explore what eigenvalues and â¦ I will post a sketch of the syllabus, along with lecture notes, below. Speaker affiliation: Henry Ford II Professor of Statistics and Data Science, Yale University. The sections of the book are drawn from my old lecture notes. Lecture 2. Course: Spectral Graph Theory from Yale. Chris Godsil and Gordon Royle, Algebraic Graph Theory. I will present a bunch of theorems, a few algorithms, and many open problems. Outline Adjacency matrix and Laplacian Intuition, spectral graph drawing Physical intuition Isomorphism testing Random walks Graph Partitioning and clustering Lecture 3. The main purpose of this course is to explore what eigenvalues and eigenvectors of graphs can tell us about their structure, and to exploit this knowledge for algorithmic purposes. Spring 2019. From Applied to Pure Mathematics Algebraic and Spectral Graph Theory Sparsification: approximating graphs by graphs with fewer edges The Kadison-Singer problem . Continuation of the Yale Probability Network Group seminar. Yale University 24 Hillhouse Avenue New Haven, CT 06511. t 203.432.0666 f 203.432.0633. Instructor: Contact AMTH 561/CPSC 662: Spectral Graph Theory. Location: Rm 107, 24 Hillhouse Ave. Speaker: Harry Zhou. Spectral and Algebraic Graph Theory Here is the current draft of Spectral and Algebraic Graph Theory, by Daniel A. Spielman. Outline Introduction to graphs Physical metaphors Laplacian matrices Spectral graph theory A very fast survey Trailer for lectures 2 and 3 . Spectral Graph Theory and its Applications Daniel A. Spielman Dept. Luca Trevisan, UC Berkeley and Bocconi University Spring 2016. To help you decide if this course is right for you, you can look at the lectures notes from the previous versions, taught in Credit only with the explicit permission of the seminar organizers. in Electrical Engineering from Rice University. It does not have many prerequisites, but it should still be viewed as an advanced course. But, it will still move at a very fast pace. CPSC 462/562 is the latest incarnation of my course course on Spectral Graph Theory. with examples from Graph Theory." Note that the undergraduate version, 462, has been approved but does not yet appear in Course Search. A Social Network Graph . Lectures and Assignments. Yale ì ê°ì Spectral Graph Theory(2018 Fall) ìë£ë¥¼ ì ë¦¬í í¬ì¤í¸ì ëë¤. DragoÅ¡ Cvetković, Peter Rowlinson, Slobodan Simić, An Introduction to the Theory of Graph â¦ Course notes from Stanford Winter 2011/2013. Course notes. Office Hours: Friday, 3:00 - 4:00 . Instructor: Dan Spielman. Spectral Theory. But, it sure beats taking notes! Whereas the previous versions, numbered AMTH 561 and CPSC 662, were essentially taught as graduate mathematics courses, this version is suitable for undergraduates and has a more applied focus. 2018, 2015, 2012, or 2009, 2004. Spectral graph theory is the interplay between linear algebra and combinatorial graph theory. This course surveys the growing field of SNA, emphasizing the merger of theory and method, while gaining hands-on experience with network data and software. (in AKW 207a) T-Th 2:30-3:45 in AKW 500 I will post a sketch of the syllabus, along with lecture notes, below. Fiedler's analysis of the eigenvectors of weighted (in AKW 207a). Topics: Many examples of graphs and Dan Spielman, Yale University Fall 2015. Analysis of algorithms and heuristics, error-correcting codes, combinatorial scientific computing, spectral graph theory, and combinatorics. The book for the course is on this webpage. NSF CCF-0634957: \Collaborative Research: Spectral Graph Theory and Its Applica- Graph partitioning in random models (Stochastic Block Models). Lecture 4. Department of Statistics and Data Science. Laplaceâs equation and its discrete form, the Laplacian matrix, appear ubiquitously in mathematical physics. And Data Science, Concentration of eigenvalues of random matrices of linear algebra or Spectral Theory. appear. Mathematics 500A the current draft of Spectral similarity for two graphs CCF-0634957: \Collaborative Research: Spectral Graph Theory very! 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