Cheeger constant (graph theory)

The Cheeger constant in graph theory is like trying to see how easy it is to break a cookie into two parts that are pretty much the same size. The cookie is a graph, which is basically a bunch of dots (called vertices) connected by lines (called edges). The Cheeger constant measures how hard it is to cut the graph into two parts that have about the same number of dots in each part, while also trying to make sure that the number of edges you cut through is pretty small. It's like trying to cut the cookie straight down the middle so you get two pieces that are almost the same size, while also trying to only break through a little bit of the chocolate chips. If it's easy to find a cut that does this, then the Cheeger constant is low. But if it's really hard to find a good cut, then the Cheeger constant is high. People who study graph theory like to know about the Cheeger constant because it tells them how closely connected the parts of a graph are, and how easy it is to break up the graph into smaller pieces.