Dots and Lines: How Maps Turn Into Graphs
Look at a subway map or the friend-connections on a game like 'who is friends with who' at recess. Grown-up mathematicians draw pictures like this using just two things: dots and lines. Each dot is a place (or a person, or a thing), and each line shows a path connecting two dots. This simple picture is called a graph, and it helps us solve real puzzles, like finding the shortest way to walk from the classroom to the lunchroom!
What You'll Learn
- What a 'dot' (called a vertex or node) represents in a graph - What a 'line' (called an edge) represents in a graph - How to count how many lines touch a single dot - How to find a path from one dot to another by following the lines
A Dot Is A Place
In a graph, every dot stands for one place or one thing. It could be your classroom, the playground, the library, and the cafeteria, each shown as its own separate dot. The dot itself doesn't tell you how big or small the real place is; it is just a marker so we can draw connections between places clearly, without a messy, complicated real map full of hallways and doors.
A Line Is A Path
A line drawn between two dots means you can travel directly between those two places without passing through any other dot first. If there is a line straight from 'Classroom' to 'Cafeteria,' that means there's a direct hallway connecting them. If there is no line between two dots, you'd have to go through a different dot to get there, the same way you might have to walk through the office to get from the gym to the art room.
Mathematicians call a dot a 'vertex' (plural: vertices) and a line a 'edge.' You can use the simple words dot and line, or the fancy math words vertex and edge, they mean exactly the same thing!
Counting Connections
Some dots have lots of lines touching them, and some have just one or two. The number of lines touching a dot is called its degree. A busy dot, like a school hallway junction where four different hallways meet, has a high degree. A dot at the very end of a single hallway, like a dead-end closet, has a degree of just 1.
Finding a Path
A path is a route you can travel by following lines from one dot to another, possibly passing through several dots along the way. If you want to go from the 'Library' dot to the 'Cafeteria' dot but there's no direct line between them, you look for a path: maybe Library connects to Hallway, and Hallway connects to Cafeteria. That chain of lines, Library-Hallway-Cafeteria, is your path.
Match each graph word to its meaning.
Terms
Definitions
Drag terms onto their definitions, or click a term then click a definition to match.
In a graph showing rooms in a school, what does a line drawn between the 'Gym' dot and the 'Playground' dot mean?
A hallway dot has 4 lines touching it, connecting to the gym, the library, the office, and the cafeteria. What is the degree of that dot?
Draw Your Classroom as a Graph
On paper, draw one dot for each important area in your home or classroom (at least 5 places, such as bedroom, kitchen, bathroom, front door, living room). Draw a line between two dots only if you can walk directly between those two places without passing through a third area first. Count and label the degree of your busiest dot. Turn in your labeled dot-and-line drawing plus one written path (a chain of at least 3 dots) from one end of your home to the other.
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