Spectral Graph Theory: Introduction

Related lectures (29)

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Explores Bourgain's theorem on sparsest cut in graphs, emphasizing semimetrics and cut optimization.

Explores the construction of Ramanujan graphs using polynomials and addresses challenges with the probabilistic method.

Explores pseudorandomness and the Expander Mixing Lemma in the context of d-regular graphs.

Explores interlacing families, Ramanujan graphs, and their construction using signed adjacency matrices.

Covers stochastic properties, network structures, models, statistics, centrality measures, and sampling methods in network data analysis.

Explores spectral clustering theory, eigenvalue decomposition, Laplacian matrix, and practical applications in identifying clusters.

Introduces network data structures, models, and analysis techniques, emphasizing permutation invariance and Erdős-Rényi networks.

Explores properties of matrices, irreducibility, and graph connectivity in networked control systems.

Explores graph theory, stochastic matrices, consensus algorithms, and spectral properties in networked control systems.

Introduces graph theory, network flows, and flow conservation laws with practical examples and theorems.