Handling Networks: Graph Theory

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Related lectures (29)

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Polynomial Identity Testing

Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.

Introduction to Networks and Brain Networks

Introduces the fundamentals of network science, focusing on brain networks and their historical breakthroughs.

Graph Algorithms: Modeling and Representation

Covers the basics of graph algorithms, focusing on modeling and representation of graphs in memory.

Stein Algorithm: Polynomial Identity Testing

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

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.

Expander Graphs: Properties and Eigenvalues

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

Subgraphs vs Induced Subgraphs

Distinguishes between subgraphs and induced subgraphs in graph theory, illustrating the construction of minimal spanning trees.

Distances and Motif Counts

Explores distances on graphs, cut norms, spanning trees, blockmodels, metrics, norms, and ERGMs in network data analysis.

Graphs and Networks: Basics and Applications

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