Imagine you have a bunch of friends who all like different things. Some of your friends like dogs, some like cats, and some like birds. Now, let's say you want to figure out if any two of your friends have similar interests. You could make a chart that shows which friends like dogs, which like cats, and which like birds. Then, you could draw lines connecting friends who like the same thing.
This chart with lines connecting friends is called a comparability graph. It helps you compare your friends' interests and see who likes the same things. If two friends are connected by a line, that means they like the same thing. If there's no line connecting them, it means they have different interests.
Comparability graphs can be used for lots of different things - not just comparing your friends' interests. They help mathematicians solve problems and find patterns in data. By drawing lines between things that are similar, they can figure out how those things are related and learn new things about the world.