Spectral Graph Theory: Introduction

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Related lectures (29)

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Convergence of Random Walks

Explores the convergence of random walks on graphs and the properties of weighted adjacency matrices.

Sparsest Cut: ARV Theorem

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.

Sparsest Cut: Leighton-Rao Algorithm

Covers the Leighton-Rao algorithm for finding the sparsest cut in a graph, focusing on its steps and theoretical foundations.

Expander Graphs: Properties and Eigenvalues

Explores expanders, Ramanujan graphs, eigenvalues, Laplacian matrices, and spectral properties.

Graphical Models: Representing Probabilistic Distributions

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

Isogenic Graphs: Spectral Analysis and Mathematical Applications

Explores isogenic graphs, spectral properties, and mathematical applications in modular forms and cryptography.

Cheeger's Inequalities

Covers Cheeger's inequalities and the combinatorial properties of graphs.

Cheeger's Inequality

Explores Cheeger's inequality and its implications in graph theory.

Matrices and Networks

Explores the application of matrices and eigendecompositions in networks.

Interlacing Families and Ramanujan Graphs

Explores interlacing families of polynomials and 1-sided Ramanujan graphs, focusing on their properties and construction methods.