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Spectral and Algebraic Graph Theory

Spectral and Algebraic Graph TheoryIncomplete Draft, dated December 4, 2019 Current version available A. SpielmanYale UniversityCopyrightc 2019 by Daniel A. Spielman. All rights ListPrefacevContentsviNotationxxiiI Introduction and Background11 Introduction22 Eigenvalues and Optimization: The Courant-Fischer Theorem213 The Laplacian and Graph Drawing274 Adjacency matrices, Eigenvalue Interlacing, and the Perron-Frobenius Theorem 325 Comparing Graphs39II The Zoo of Graphs466 Fundamental Graphs477 Cayley Graphs558 Eigenvalues of Random Graphs639 Strongly Regular Graphs73iCHAPTER LISTiiIII Physical Metaphors8210 Random Walks on Graphs8311 Walks, Springs, and Resistor Networks9312 Effective Resistance and Schur Complements10113 Random Spanning Trees11014 Approximating Effective Resistances11715 Tutte s Theorem: How to draw a graph12216 The Lov`asz - Simonovits Approach to Random Walks13017 Monotonicity and its Failures13518 Dynamic and Nonlinear Networks143IV Spectra and Graph Structure15119 Independent Sets and Coloring15220 Graph Partitioning15921 Cheeger s Inequality16422 Local Graph Clustering16923 Spectral Partitioning in a Stochastic Block Model17724 Nodal Domains18425 The Second Eigenvalue of Planar Graphs19226 Planar Graphs 2, the Colin de Verdi`ere Number199 CHAPTER LISTiiiV Expander Graphs20627 Properties of Expander Graphs20728 A brief introduction to Coding Theory21629 Expa

\Applied Numerical Linear Algebra" by James W. Demmel For those needing an introduction to linear algebra, a perspective that is compatible with this book is contained in Gil Strang’s \Introduction to Linear Algebra." For more advanced topics in linear algebra, I recommend \Matrix Analysis" by Roger Horn and Charles Johnson, as well as

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