Lectures related to Matrix Tree Theorem

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

Explores graphs and matrices, including adjacency, degree, and Laplace matrices, Matrix-tree theorem, and spanning trees.

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

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

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

Explores graph traversal methods, spanning trees, and shortest paths using BFS and DFS.

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

Introduces Spectral Graph Theory, exploring eigenvalues and eigenvectors' role in graph properties.

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

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

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

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

Explores the application of matrices and eigendecompositions in networks.

Explores coordination in networked control systems, graph theory, and consensus algorithms.

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

Introduces the basics of graphs and networks, covering definitions, paths, trees, flows, circulation, and spanning trees.

Covers graphical models for probability distributions and factor graphs representation.

Introduces elementary graph algorithms, focusing on Breadth-First Search and Depth-First Search.

Explores Laplacian matrix properties in networked control systems and their relation to graph theory.

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