Lectures on Spectral Graph Theory by Fan R. K. Chung

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Lectures on Spectral Graph Theory written by Fan R. K. Chung
. This is an other great mathematics book cover the following topics.

1. Eigenvalues and the Laplacian of a graph 1.1. Introduction 1
1.2. The Laplacian and eigenvalues 2
1.3. Basic facts about the spectrum of a graph 6
1.4. Eigenvalues of weighted graphs 11
1.5. Eigenvalues and random walks 14

2. Isoperimetric problems 2.1. History 23
2.2. The Cheeger constant of a graph 24
2.3. The edge expansion of a graph 25
2.4. The vertex expansion of a graph 29
2.5. A characterization of the Cheeger constant 32
2.6. Isoperimetric inequalities for cartesian products 36

3. Diameters and eigenvalues 3.1. The diameter of a graph 43
3.2. Eigenvalues and distances between two subsets 45
3.3. Eigenvalues and distances among many subsets 49
3.4. Eigenvalue upper bounds for manifolds 50

4. Paths, flows, and routing 4.1. Paths and sets of paths 59
4.2. Flows and Cheeger constants 60
4.3. Eigenvalues and routes with small congestion 62
4.4. Routing in graphs 64
4.5. Comparison theorems 68

5. Eigenvalues and quasi-randomness 5.1. Quasi-randomness 73
5.2. The discrepancy property 75
5.3. The deviation of a graph 81
5.4. Quasi-random graphs 85