Introduction to Graph Theory

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Graph Theory Concepts and Terminology

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:01 Graph Theory
  • 0:56 A Graph
  • 1:44 Vertices
  • 2:34 Edges
  • 3:15 Loops
  • 3:47 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Speed Speed Audio mode
Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will understand what graph theory is. You will also see what a graph looks like and be introduced to the basic vocabulary used in graph theory.

Graph Theory

In math, there is a whole branch of study devoted to graph theory. What is it? It is the study of graphs. Yes, you may not believe that graphs can be so complicated, but as you will see, the study of graphs and how they connect is a big field of study. So big, in fact, that big businesses as well as public transportation companies spend much time on graph theory to make sure that everything functions smoothly.

For example, utility companies, such as those that supply electricity, rely on graph theory when setting up their power poles to make sure the poles are located in the best possible location in relation to all the other poles. Public transportation companies, such as buses, use graph theory to plan the best possible route between a number of destinations. Yes, all of these use graph theory. If you look at a map and you try to plan a route from point A to point B, you yourself are practicing graph theory.

A Graph

If you were to draw a simplified version of your map, you would have points for your cities and straight lines connecting the dots representing roads. This simplified version of your map is the kind of graph that you will see in graph theory:

Graph theory map
graph theory

If this graph is a simplified version of our map, then we see that we have four cities - the four points - and five roads - the five straight lines. Graph theory then is about studying this graph and seeing what is the best possible route to take between any two points in this graph. Public transportation companies can use this graph to find the best possible route between points A and C, for example. Utility companies can use this graph to determine which poles are connected to each other and how best to supply power to all the poles.


Now, for the vocabulary. Notice the points A, B, C, and D. These points are called vertices in graph theory. When we have several points, we have vertices. If we have just one point, we call it a vertex. Vertices are the points that lines come and go from. Some vertices can have just one line connecting to it. Others can have several lines connecting to other vertices. For example, in our graph, points A and C both have two lines connecting them to other points. Points B and D, on the other hand, have three lines. In graph theory, you can have an unlimited number of lines connecting one point to other points. The graph we have here is a very simple graph just to get us started in learning about graph theory.

To unlock this lesson you must be a Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use

Become a member and start learning now.
Become a Member  Back
What teachers are saying about
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account