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Spectral Graph Theory

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Master eigenvalues, Laplacian matrices, and graph connectivity to solve complex network problems in computer science and physics. Access advanced mathematical lectures from leading research institutes on YouTube and Swayam, covering spectral methods, algebraic graph theory, and applications to algorithms and neural networks.

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BIMSA
Equiangular Lines and Eigenvalue Multiplicity - ICBS 2024

Explore equiangular lines in high dimensions, solving a longstanding problem using spectral graph theory and discussing future research directions.
- YouTube
- 56 minutes
- On-Demand
- Free Video
Centre de recherches mathématiques - CRM
Exponentially Many Graphs Are Determined by Their Spectrum

Explore discrete analogues of Kac's question on "hearing the shape of a drum" and learn about graphs determined by their spectrum in this mathematical seminar.
- YouTube
- 49 minutes
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Simons Institute
Online Algorithms for Spectral Hypergraph Sparsification

Explore online algorithms for spectral hypergraph sparsification, focusing on space-efficient methods for handling streaming hyperedges and producing accurate sparsifiers.
- YouTube
- 32 minutes
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- Free Video
International Centre for Theoretical Sciences
Spectral Refutations and Their Applications to Algorithms and Combinatorics - Lecture 2

Explore spectral refutation techniques and their powerful applications in algorithmic design and combinatorial problem-solving through advanced mathematical frameworks.
- YouTube
- 1 hour 13 minutes
- On-Demand
- Free Video
NPTEL-NOC IITM
Introduction to Cospectral Graphs

Discover cospectral graphs through adjacency and Laplacian matrices, exploring when different graphs share identical eigenvalue spectra.
- YouTube
- 32 minutes
- On-Demand
- Free Video
NPTEL-NOC IITM
A Bound on the Diameter of a Graph Using the Number of Distinct Eigenvalues

Discover how graph diameter relates to distinct eigenvalues of adjacency matrices through mathematical bounds and proofs.
- YouTube
- 31 minutes
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- Free Video
BIMSA
Connection Laplacian on Discrete Tori with Converging Property

Explore connection Laplacians on discrete tori and their convergence properties in this advanced mathematical analysis presented at ICBS2025.
- YouTube
- 55 minutes
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Conference GSI
Perturbation of Fiedler Vector: Interest for Graph Measures and Shape Analysis

Explore Fiedler vector perturbation and its applications in graph measures and shape analysis, gaining insights into advanced mathematical concepts.
- YouTube
- 21 minutes
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Institute for Advanced Study
A New Approach to Strong Convergence - Lecture 1

Explore a novel approach to strong convergence in graph theory, addressing Alon's conjecture and extending Friedman's theorem with applications to random graphs, geometry, and operator algebras.
- YouTube
- 2 hours 7 minutes
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NPTEL-NOC IITM
Upper Bound on Algebraic Connectivity

Discover how to establish upper bounds on algebraic connectivity through Fiedler vector analysis and induced subgraph decomposition techniques.
- YouTube
- 21 minutes
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NPTEL-NOC IITM
Introduction to Algebraic Connectivity and Fiedler Vector

Discover algebraic connectivity and Fiedler vectors through Laplacian matrix eigenvalues and their corresponding eigenvectors in graph theory.
- YouTube
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NPTEL-NOC IITM
Some More Bounds on Algebraic Connectivity

Explore advanced upper bounds on algebraic connectivity for connected and regular graphs, including relationships with graph expansion ratios.
- YouTube
- 20 minutes
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NPTEL-NOC IITM
Relation Between Algebraic Connectivity of Graph and Its Induced Subgraph

Explore the mathematical relationship between a graph's algebraic connectivity and its induced subgraphs in this focused mathematical analysis.
- YouTube
- 16 minutes
- On-Demand
- Free Video
International Centre for Theoretical Sciences
Spectral Graph Theory - Lecture 1

Explore spectral graph theory, covering self-adjoint matrices, Rayleigh equalities, graph isomorphism, Cayley graphs, and automorphism groups. Gain insights into complex systems and network analysis.
- YouTube
- 1 hour 31 minutes
- On-Demand
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Ryan O'Donnell
Spectral Graph Theory - Eigenvalues at CMU - Lecture 15a of CS Theory Toolkit

Explore eigenvalues of the Laplacian and Markov operator in spectral graph theory, including associated formulas and their applications in theoretical computer science research.
- YouTube
- 22 minutes
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