Graph Algorithms: Basics

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Related lectures (50)

Graph Theory and Network Flows Log in to Mediaspace to watch this video

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

Expander Graphs: Properties and Eigenvalues Log in to Mediaspace to watch this video

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

Graphical Models: Probability Distributions and Factor Graphs Log in to Mediaspace to watch this video

Covers graphical models for probability distributions and factor graphs representation.

Graph Neural Networks: Interconnected World Log in to Mediaspace to watch this video

Explores learning from interconnected data with graphs, covering modern ML research goals, pioneering methods, interdisciplinary applications, and democratization of graph ML.

Independence Polynomial of Dependency Graph Log in to Mediaspace to watch this video

Covers the independence polynomial of a dependency graph and related concepts such as graph coloring and directed graph properties.

Learning from the Interconnected World with Graphs Log in to Mediaspace to watch this video

Explores learning from interconnected data using graphs, covering challenges, GNN design, research landscapes, and democratization of Graph ML.

Convergence of Random Walks Log in to Mediaspace to watch this video

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

Pseudorandomness: Expander Mixing Lemma Log in to Mediaspace to watch this video

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

Bellman Ford Algorithm Log in to Mediaspace to watch this video

Explores the Bellman Ford algorithm for finding the shortest path in graphs with negative edge weights.

Isogenic Graphs: Spectral Analysis and Mathematical Applications Log in to Mediaspace to watch this video

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

Network Flows Meets Simplex Log in to Mediaspace to watch this video

Explores network flows, simplex method, linear programming, tree solutions, and dual solutions in optimization problems.

Topological Sort and SCC Log in to Mediaspace to watch this video

Explores topological sort, acyclic graphs, Strongly Connected Components, magic algorithm, component graph, flow networks, and their applications.

Sparsest Cut: Leighton-Rao Algorithm Log in to Mediaspace to watch this video

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

Differentiable Functions and Lagrange Multipliers Log in to Mediaspace to watch this video

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Link-based Ranking: Graph Mining Log in to Mediaspace to watch this video

Explores link-based ranking and graph mining techniques for efficient web graph analysis.

Graph Theory Fundamentals Log in to Mediaspace to watch this video

Explores fundamental graph theory concepts, Erdős' results, Chromatic Lemma, and Union Bound theorem in graph theory.

Interlacing Families and Ramanujan Graphs Log in to Mediaspace to watch this video

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

Cheeger's Inequality Log in to Mediaspace to watch this video

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

Physarum can compute shortest paths Log in to Mediaspace to watch this video

Explores how Physarum Polycephalum can compute shortest paths in a directed graph model.

Translations and Homotheties Log in to Mediaspace to watch this video

Covers translations, homotheties, and geometric transformations using vectors and matrices.

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