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Concept

Spectral graph theory

Related lectures (32)

Consensus Algorithms: Weight Assignment and Applications

Explores the design of graph weights for consensus and applications in sensor networks.

Distributed Computation: Consensus Algorithms in Networked Control Systems

Explores consensus algorithms in networked control systems, covering topics like Metropolis-Hasting models and distributed computation of Least-Squares regression.

Cheeger's Inequalities

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

Algebraic Graph Theory: Matrices and Connectivity

Explores algebraic graph theory applied to networked control systems and consensus algorithms.

Networked Control Systems: Laplacian Flow and Heat Equation

Explores Laplacian flow, heat equation analogies, and microgrid networked controllers.

Graph Models and Brain Connectomics

Explores graph theory in brain connectomics, MRI applications, network analysis relevance, and individual fingerprinting.

Spectral Graph Theory: Introduction

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

Non-parametric regression for networks

Explores non-parametric regression for networks, covering object data analysis, network graphs, extrinsic distances, and practical projections.

Networked Control Systems: Laplacian Matrix and Consensus

Explores the Laplacian matrix and consensus in networked control systems.

Belief Propagation

Explores Belief Propagation in graphical models, factor graphs, spin glass examples, Boltzmann distributions, and graph coloring properties.

Graph Alignment: Wasserstein-based

Discusses challenges in comparing non-Euclidean data, proposing a Laplacian-based solution for graph alignment and exploring optimal transport for graph distance computation.

Graph Isomorphisms

Covers the concept of graph isomorphisms, explaining the definition, notation, examples, computational complexity, and number of isomorphism classes.

Sparsest Cut: ARV Theorem Log in to Mediaspace to watch this video

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.

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.

Pseudorandomness: Theory and Applications Log in to Mediaspace to watch this video

Explores pseudorandomness theory, AI challenges, pseudo-random graphs, random walks, and matrix properties.

Ramanujan Graphs: Generating Functions and Expander Graphs Log in to Mediaspace to watch this video

Explores Ramanujan graphs, generating functions, non-backtracking walks, and expander graphs in relation to NP-hard problems.

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

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

Bipartite Graphs: Independent Sets Log in to Mediaspace to watch this video

Explores bipartite graphs, independent sets, Shearer's Lemma, labeled graphs, and entropy analysis.

Sparsest Cut and Concurrent Flow Log in to Mediaspace to watch this video

Covers sparsest cut, NP-completeness, Bougains Theorem, and concurrent flow in graphs.

Graphs and Phase: Understanding Amplitude and Phase Relationships Log in to Mediaspace to watch this video

Analyzes amplitude and phase graphs, emphasizing force concentration and phase shift.