Concept

Spectral graph theory

Related lectures (32)

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

Positive Definite Coxeter Graphs

Explores the classification of positive definite connected Coxeter graphs through detailed calculations and proofs.

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.

Sparsest Cut: Bourgain's Theorem

Explores Bourgain's theorem on sparsest cut in graphs, emphasizing semimetrics and cut optimization.

Convergence of Random Walks

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

Network Sampling: Consistency, Models, and Dynamics

Explores network sampling consistency, models, and graph dynamics in real-life scenarios.

Network clustering

Explores network clustering, spectral clustering, k-means algorithm, eigenvalue properties, block model estimation, and structural similarity measurement.

Graph Isomorphisms

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

Eigenvalues and Sequences

Discusses finding d-regular graphs with specific eigenvalue properties and the existence of Ramasugan sequences for d-opt prime numbers.

Isomorphic Graphs: Definition and Examples

Explains isomorphic graphs through examples and the relationship with identical graphs.

Cheeger's Inequalities

Explores Cheeger's inequalities for random walks on graphs and their implications.

Building Ramanujan Graphs

Explores the construction of Ramanujan graphs using polynomials and addresses challenges with the probabilistic method.