Algebraic Graph Theory Courses and Certifications

Ryan O'Donnell

High-Dimensional Expanders - How I Learned to Stop Worrying and Love Group-Theoretic Constructions

A research talk on constructing high-dimensional expanders from Chevalley groups using spectral expansion and coset complexes.

• YouTube
• 47 minutes
• Self-Paced
• Free Video

Ryan O'Donnell

Spectral Graph Theory - Eigenvalues at CMU - Lecture 15a of CS Theory Toolkit

Explores Laplacian and Markov-operator eigenvalues and eigenvectors in graphs, connecting spectral formulas to conductance and random-walk convergence.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

Ryan O'Donnell

Spectral Graph Theory - Minimizing/Maximizing the Quadratic Form

Analyze how graph quadratic forms are minimized and maximized, connecting their extremal values to connected components and bipartiteness.

• YouTube
• 33 minutes
• Self-Paced
• Free Video

Ryan O'Donnell

Spectral Graph Theory - The Quadratic Form

Introduces the graph quadratic form as an edge-based measure of variation, connecting indicator functions to edge boundaries and cuts.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

Insights into Mathematics

The Pentagon and Numbers Games - A Dualization of the Mutation Game

Explore the Pentagon Game and Numbers Game, and their precise duality with mutation games on graphs.

• YouTube
• 23 minutes
• Self-Paced
• Free Video

Ryan O'Donnell

Expander Graph Constructions - Lecture of CS Theory Toolkit

Surveys explicit constructions of expander graphs, including Margulis–Gabber–Galil, Ramanujan, and Zig-Zag product expanders.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

NPTEL-NOC IITM

Introduction to Algebraic Graph Theory

Discover the fundamental concepts of algebraic graph theory, exploring how algebraic methods apply to graph structures and their mathematical properties.

• YouTube
• 11 minutes
• Self-Paced
• Free Video

Mathematics of Big Data and Machine Learning

Learn D4M, a signal-processing approach that combines graph algorithms, linear algebra, and databases for big-data and machine-learning problems.

• MIT OpenCourseWare
• Self-Paced
• Free Online Course

Introduction to Multi-Agent Systems

Study networked dynamical systems, graph theory, controllability, and consensus protocols for coordinated robots, autonomous vehicles, oscillator networks, and social networks.

• Swayam
• 12 weeks
• Available until Oct 9, 2026
• Free Online Course

Aleksa Gordić - The AI Epiphany

Graph Convolutional Networks - GNN Paper Explained

A deep dive into graph convolutional networks through spectral, Weisfeiler–Lehman, and message-passing perspectives.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Introduction to Algebraic Graph Theory

Learn to analyze graph properties and derive graph-theoretic bounds using eigenvalues, matrices, and other algebraic techniques.

• Swayam
• 8 weeks
• No Longer Offered
• Free Online Course

Insights into Mathematics

Exceptional Structures in Mathematics and Physics From Dynamics on Graphs

Explore how graph games generate exceptional structures such as the E8 root system and its symmetries.

• YouTube
• 35 minutes
• Self-Paced
• Free Video

NPTEL-NOC IITM

Introduction to Ramanujan Graphs

Discover optimal expander graphs through Ramanujan graphs and explore Margulis construction methods for creating these mathematically significant structures.

• YouTube
• 20 minutes
• Self-Paced
• Free Video

NPTEL-NOC IITM

Strongly Regular Graphs - Their Eigenvalues and Characterization

Discover strongly regular graphs through eigenvalue calculations and mathematical characterization techniques in this focused mathematical exploration.

• YouTube
• 31 minutes
• Self-Paced
• Free Video

Алгебраическая теория графов

Изучение универсальных структур графов и их применение в различных областях науки. Развитие математического мышления через анализ свойств графов и решение практических задач.

• Coursera
• 6 weeks
• No Longer Offered
• Paid Course