1736
Euler solved the Königsberg bridges problem
It launched graph theory. Today, every map and dependency tree is still composed of vertices and edges.
Graph theory · Udemy course
Graph theory,
from basics to advanced topics
A structured journey from first definitions to matching, coloring, and algorithms. Delivered as a course you can stream anytime, with exercises, comments and solutions.
- Sections
- 12
- Hours
- 9+
- Quizzes
- 60
Why learn graph theory?
It’s the key to hidden structures
There is a graph hidden in every network, roadmap, and dependency. Learn the vocabulary once: circuits, planarity, transversals, and you’ll recognize the patterns across operations, research and everyday habits.
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Symbols that matter
Graphs can be studied in many different ways. They yield very interesting properties. Many of them are interconnected and have many practical applications.
4
Four color theorem
Any political map can be coloured using four colours. There are some exceptions to this rule, which you will learn about in the course.
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Paths to analyze
A courier delivering goods to twelve customers can plan the order of visited points in so many ways Each additional customer drastically increases this number.
Why this course?
Serious math, packaged for how people actually watch courses today
On-demand access
Watch on web or in the mobile app. Pause, replay, and learn at the pace that fits your schedule.
Intuition first
Pictures before formalism. Then we tighten definitions and proofs, so the ideas can be transferred.
Practice as you go
Quizzes and problem sets after the major topics, so you can apply what you just learned in the lectures.
Curriculum
Twelve sections. Each with a clear milestone
Engaging lectures and short quizzes. Jump to what you need, or follow the path from start to finish. Solve problem sets to consolidate your knowledge. Review comments and solutions.
Introduction & foundations
Vertices, edges, isomorphism, and matrix representation. The language used across all of graph theory.
Graph examples & connectivity
Properties of complete, linear, bipartite, and wheel graphs. The concepts of subgraphs, line graphs, vertex and edge connectivity.
Eulerian & Hamiltonian circuits
Euler's theorem, Fleury's algorithm. Sufficient and necessary conditions. Dirac's and Ore's theorems.
Classical problems & trees
Shortest path problem, salesman problem and knight's tour problem will be presented. We will learn the properties of trees and become skilled at proving theorems.
Planarity & coloring
We'll learn tools that can help us diagnose whether a given graph is planar or not. We'll colour vertices, edges, faces in the graph and then explore the consequences.
Directed graphs & matching
We'll learn tools that can help us diagnose whether a given graph is planar or not. We'll colour vertices, edges, faces in the graph and then explore the consequences.
About the author
The person behind the syllabus
Jakub Nowak
Instructor of Graph Theory
I created this course because graph theory is everywhere, but it’s often taught as a pile of definitions instead of a toolkit. My goal is to get you to see the graphs in the wild: roads, schedules, constraints, networks, and then reach for the right theorem or algorithm with confidence.
My background blends mathematics and algorithms with years of teaching experience, breaking concepts into diagrams, examples and funfacts.
If you’ve ever felt lost in a notation-heavy textbook, this course is the opposite: intuition first, rigor second.
- Valuable knowledge to boost your career
- Visual proofs that make the concepts easy to understand
- Practice with quizzes and problem sets after each major topic
- Clear explanations and visualizations
Enroll when you are ready
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