Graph Theory Online Courses & Lessons (Free + Paid)

Graph Theory Courses
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Graph theory has more computational application than we know. Take any of these graph theory courses to understand it in detail. Coursera’s graph theory course could be one of the best one for overall learning.

In this world, there are umpteen problems. Some are scientific, mathematical, or business problems. One of the best ways to find a way out of these situations is to get an optimal solution. So, with graph theory courses, you will enter into the journey of mathematical concepts and graphs that can help you solve some everyday problems.


Graph Theory is a fascinating subject that connects the rigor of mathematics and the elegance of painting. It is an advanced concept in mathematics. At the university level, senior students majoring in Computer Science and Mathematics take this class for sure. Even though it is pretty straightforward, it is not unsophisticated.


With Graph Theory, you learn to represent pictorially several significant mathematical insights and results into the deep theories behind them. However, it is not a complicated subject provided you access the correct knowledge. We tell you about some of the best courses on the internet to master this subject.



Overall Best Course Introduction to Graph Theory Offered by University of California San Diego – [Coursera]

Overall Best Course

Why this course?

It is the best graph theory course for beginners, wherein you study with the University of California San Diego Alumni. This class is for everyone who wishes to work in IT or those currently working in TV. Even motivated high school students will love this class.


Things you may like

  1. It is a 100% online class with flexible deadlines. So you can set and reset the deadlines in your schedule.
  2. You can start the course anytime and learn at your pace.
  3. You will earn a shareable certificate after finishing the session.
  4. It is a beginner-friendly session.


Things you may not like

  1. There are some prerequisites. Hence, you must be well-versed in basic math. So, you must know what a square is or how to add fractions. In addition, knowledge of basic Python programming (functions, loops, recursion) is a must.


About the course

It is one of Coursera’s top-selling courses for graph theory, wherein you will learn how GPS systems locate the shortest routes. In addition, you will also understand how biologists assemble genomes, how engineers design integrated circuits, and why a political map is colored using only a few colors.


You will also study the Ramsey Theory that proves how a complete disorder is impossible in a big system. Once the session ends, you can implement the algorithm that finds an optimal assignment of students to schools.


Developed by Lloyd S. Shapley and David Gale, this algorithm was recognized by the Nobel Prize in Economics conferral. It takes twenty-one hours to complete and is Course 3 of 5 in the Introduction to Discrete Mathematics for Computer Science Specialization.


Reviews By YZ

This course is interesting, and it is a good introduction. I like the first four weeks’ courses, while I feel the last week’s course is not clear presented, which changes the instructor.



Most Prestigious Course Graph Theory and Additive Combinatorics Offered by Massachusetts Institute of Technology – [MIT Open Course Ware]

Most Prestigious Course

Why this course?

You will study with Prof. Yufei Zhao, Associate Professor of Mathematics, Department of Mathematics, Massachusetts Institute of Technology. So, if you believe in learning from the best, this can be the course for you.


Things you may like

  1. There are no exams. Your grades will depend on your participation.
  2. You will work on several practical problems with real world exposure.


Things you may not like

  1. If you are not well-versed in the mathematical maturity of the first-year math graduate student, you may be unable to excel in this course.


About the course

In this graph theory online course, you will study the modern and classical developments in graph theory and additive combinatorics with themes and topics that connect the two subjects. In addition, this class will introduce you to current research topics and open problems. It is a two-session class per week course with 1.5 hours per session.


In this class, you will study the modern and classical developments in additive combinatorics and graph theory. The focus is on themes and topics that connect the two subjects. Further, the instructor also introduces students to current research topics and open problems in the session.


Moreover, you will develop Roth’s theorem understanding sans a 3-term arithmetic progression containing o(N) elements. Beyond this, you will see different proofs of Roth’s theorem: 1) Roth’s original Fourier analytic approach and 2) a graph theoretic approach. Your final grade will depend on the minimum of the student’s performance in the two categories:


  1. Problem sets: 6 problem sets
  2. Writing assignments: (1) course notes and (2) Wikipedia contributions



Best Graph Theory Free Online Course Introduction To Graph Theory – [Alison]

Best Graph Theory Free Online Course

Why this course?

It can be a good pick if you need a free online certification class.


Things you may like

  1. It is a video-based class for professionals with a background and even beginners.
  2. The instructor presents the graphs from the computer science perspective and presents graph theory in simple language.
  3. You get a free certification with CPD accreditation.


Things you may not like

  1. None.


About the course

A graph helps you identify a problem and also focusses on finding the best solution with minimum effort. In this session, you will understand what graphs actually mean, their types, and the difference between multiple kinds of graphs.


In the first section, you will learn to answer vital graph-related questions, which sets the pace for the class. As you progress, you will gain insights on trees, including the lowest common ancestors (LCA) and isomorphic trees.


Further, when you proceed forward, you will learn about topological sorting, Dijkstra’s Shortest Path, and the Bellman-Ford and Floyd Warshall algorithms.


In this session, you will understand the graphs within the context of computer science. You will also review various network flow topics like the Ford Fulkerson algorithm for max flow, bipartite matching, and capacity scaling. You can complete the session in 4 to 5 hours.



Training for Basics Graph Theory – [Udemy]

Training for Basics

Why this course?

You get lifetime access to the lectures of these graph theory courses. So, anytime an instructor adds new concepts to the course, you will have access to them, too, without spending an extra penny.


Things you may like

  1. There are no prerequisites except elementary knowledge of mathematical operations like multiplication and addition. Hence, you can learn Graph theory sans any advanced Mathematical background.
  2. It progresses gradually, starting from the 12th graders level because the class commences with the basic idea and then to more complex topics.
  3. The class has multiple quizzes after every lecture to test what you have learned.
  4. There is a dedicated Q&A section with support.
  5. You can view it on your TV and mobile.
  6. After you complete, you receive a certificate of completion.
  7. The class comes with a 30-day money-back guarantee.
  8. The course is imparted in simple English, away from cloudy, complicated mathematical jargon.


Things you may not like

  1. The lecturer speaks too fast.
  2. There is a repetition in some parts.


About the course

In this course, you will learn to master the fundamental Graph theory concepts and understand graph coloring. Further, you will develop an understanding of Hamiltonian and Eulerian circuits and paths and several topics associated with Paths.


You will study different graphs, and their properties and perform elementary and advanced operations on them to produce a new graph.


As you progress, you will also know how to turn a graph into a matrix and vice versa. Finally, you will acquire a solid foundation in Trees, Tree Traversals, and Expression Trees.


Reviews By Jovin Leong Wei Jie

Not bad; delivers on the subject but could do with more practices beyond the quizzes like actual graph problems to solve.



Best for Advanced Learning Advanced Algorithmics and Graph Theory with Python – Offered by Institut Mines-Télécom Atlantique – [edX]

Best for Advanced Learning

Why this course?

In this graph theory online course, you can solidify your understanding of graph theory and algorithms and gather experience in Python along the way. Over 16,000 students took this class to authenticate this claim.


Things you may like

  1. It is a short six-week session and demands an effort of two to four hours every week.
  2. It is a self-paced session. So you can progress at your pace.
  3. You can get the free version, but an optional upgrade is available at a small fee.


Things you may not like

  1. In the free version, there will be no graded assignments or certifications.
  2. It is an intermediate-level session. So, you must possess a familiarity with Python 3 and basic mathematics.
  3. The class is not accessible to learners in Iran, Cuba, and the Crimea region of Ukraine.


About the course

Programming and algorithms are vital skills for engineering students, computer developers, data scientists, analysts, and hobbyists. However, understanding how to program algorithms can be a tedious task, especially if you do not get an opportunity to practice what you learn. So, as part of this session, you will focus on more than the theoretical concepts and procedures.


The instructor provides a challenge wherein you will have to beat an algorithm by coming up with a clever solution of your own. It implies that you will have to devise a faster route than your opponent via a maze when picking the objects.


Every week you will learn new concepts and materials to better your artificial intelligence and beat your opponent. Hence, as a learner, you will confront every abstract notion with a real-world problem. These graph theory courses have received financial support from the Patrick and Lina Drahi Foundation.


The class teaches you the following:

  1. How to express a computational problem (such as pathfinding) with graph theory?
  2. Choosing the correct algorithm for solving the given computational problem.
  3. Coding the algorithmic solution in Python
  4. Methods to evaluate the proposed solution in terms of its complexity.



Best for All Levels Graph Theory Algorithms – [Udemy]

Best for All Levels

Why this course?

It is one of the highest-rated classes on Udemy. If you have the necessary exposure to computer science fundamentals (e.g., data structures, recursion, classes, OOP), you will love this class.


Things you may like

  1. In this course, you receive a complete introduction to Graph Theory algorithms in computer science.
  2. Anyone seeking a comprehensive session on graph theory can opt for this class.
  3. It comes with lifetime access.
  4. There is a certificate of completion.
  5. You get a 30-day money-back guarantee.


Things you may not like

  1. It does not discuss real-world problems.


About the course

It is a comprehensive class, and you will learn several things in these graph theory lessons. These include:

  1. Representation and storage of graphs on a computer
  2. Depth-first search algorithm
  3. Breadth-first search algorithm
  4. Common graph theory problems
  5. Topological sort algorithm
  6. Various tree algorithms, including the height of a tree, finding the center of a tree, rooting a tree, etc
  7. Floyd-Warshall all pairs shortest path algorithm
  8. Traveling salesman problem (TSP)
  9. Dijkstra’s algorithm
  10. Finding bipartite graph matchings
  11. Bellman Ford’s algorithm
  12. The Lowest Common Ancestor (LCA) Problem
  13. Finding strongly connected components (Tarjan’s)
  14. Finding bridges/articulation points
  15. Shortest/longest path on an acyclic graph
  16. And more


Reviews By Dean M.

Seems to be good so far.



Course Selection Methodology

So, these are the six best graph theory courses. They are all top-notch classes, one better than the other. Hence, your selection depends on the aspect you give preference over the other.


We considered the following factors for the selection of these six courses:


1. Comprehensiveness – We have ensured that we pick only the classes that offer detailed and complete information because we know nobody wishes to take incomplete courses to acquire knowledge on the subject.

2. Fluency –The instructor’s fluency, experience, background, and knowledge of the subject are other factors. All of our listed classes above are presented by instructors who know what they speak and are well-acquainted with Graph Theory.

3. Reviews – We read through the reviews from the students who took this class in the past and only chose the ones with high reviews and ratings.

4. Certification – The certificate offers authentication for the class and an instrument for career advancement for learners. So, the majority of the listings above come with accreditation.


Frequently Asked Questions

Ques 1. What should I study before graph theory?

Ans. It helps to be well-versed in mathematics before studying graph theory. So, you can take a course in elementary number theory and basic set operations in Mathematics before Graph theory.


Ques 2. Do you need linear algebra for graph theory?

Ans. In most graph theory sessions, the instructor presumes the learner’s familiarity with linear algebra and basic counting methods such as binomial coefficients. So, it’s good to have some pre-hand knowledge in algebra.


Ques 3. Is graph theory math or computer science?

Ans. It is a blend of both math and computer science.


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