
In this lecture, we introduce the concept of a graph in graph theory and we describe its main elements.
We explain in detail how to represent graphs and look at some examples.
We explain in detail how to represent graphs and look at some examples.
In this lecture, we study the concept of degree and graph theory.
We study the representation method using the Adjacency Matrix.
We study the representation method using the Incidence Matrix.
We explain how to represent graphs using Incidence Lists.
In this lecture, we study the variants in the definition of a graph.
In this lecture, we delve into the concept of degree and study some important aspects of graph theory.
In this lecture, we study the handshaking lemma in graph theory.
In this lecture, we see an application of the handshaking lemma to regular graphs.
In this lecture we study the main types of graphs.
In this lecture, we define the concept of isomorphisms in graph theory.
In this lecture, we solve problem 1 from the section on the fundamentals of graph theory.
In this lecture, we solve problem 2 from the section on the fundamentals of graph theory.
In this lecture, we study subgraphs in graph theory.
In this lecture, we study derived graphs in graph theory.
In this lecture, we study the main operations on graphs.
In this lecture, we study walks in graph theory and explore some examples of specific paths.
In this lecture, we study connected graphs in graph theory.
In this lecture, we study some fundamental propositions about connected components and connected graphs.
In this lecture, we introduce cut vertices (or articulation points) and bridges (or cut edges) in graph theory.
In this lecture, we make a brief introduction to the concept of distance in graph theory.
In this lecture, we study the concept of eccentricity of a vertex in graph theory.
In this lecture, we study the concept of diameter.
In this lecture, we introduce Eulerian graphs.
In this lecture, we study a fundamental theorem of Eulerian graphs.
In this lecture, we study Fleury's algorithm.
In this lecture, we make a brief introduction to Hamiltonian graphs.
In this lecture, we study an important aspect of graphs that are both bipartite and Hamiltonian.
In this lecture, we study Ore's theorem.
In this lecture, we study Dirac's theorem.
Welcome to The Complete Graph Theory Course: From Zero to Hero! — your all-in-one guide to mastering the fascinating world of graph theory, from the very basics to advanced concepts. Whether you're a complete beginner or someone looking to solidify and expand your understanding, this course is designed to take you step by step through the essential ideas, techniques, and applications that make graph theory such a powerful and widely applicable field.
Graph theory is everywhere — in computer science, mathematics, network design, linguistics, biology, social sciences, and beyond. It provides a universal language for modeling relationships, designing algorithms, and analyzing systems in a structured, logical way. In this course, you’ll develop a deep and intuitive understanding of graphs, learning not only how to define and work with them, but also how to uncover their hidden patterns and apply them to real-world scenarios.
We begin from scratch: what graphs are, how they are represented, and the many types you’ll encounter — including simple graphs, multigraphs, directed graphs, and weighted graphs. We then explore core terminology and foundational properties, such as vertices, edges, degrees, adjacency, incidence, and subgraphs.
As the course progresses, we dive into more advanced topics like walks, paths, cycles, connectivity, trees, isomorphisms, spanning trees, and graph cuts. You’ll learn to spot structural patterns, reason about connectivity, and develop the tools to prove key results rigorously. Whether you're analyzing a social network, mapping a transportation system, or designing efficient algorithms, you'll gain the insight needed to approach problems graph-theoretically.
This is not just a theory-heavy course. Concepts are consistently motivated with practical examples, intuitive explanations, and problem-solving strategies. Each lecture is crafted to combine clarity with depth, helping you build confidence without being overwhelmed. Exercises and examples are carefully chosen to reinforce understanding and prepare you for further study or academic work.
What if I get stuck?
You won’t be alone.
I offer fast, friendly, and personalized support — 7 days a week — so you’ll never feel stuck or left behind. Ask questions, share your doubts, and get clear explanations to keep your learning on track.
There’s no risk either!
There’s zero risk in enrolling.
This course comes with a 30-day money-back guarantee. If you're not completely satisfied with the course or your progress, just let me know — and you'll receive a full refund, no questions asked.
You either finish the course with strong graph theory skills and a deeper understanding of one of the most important fields in mathematics and computer science — or you get your money back.
You truly have nothing to lose, and a whole new way of thinking to gain.
Let’s go from zero to hero in graph theory — together!