Independent sets

An independent set in a graph is a group of points (or vertices) where no two points are directly connected by a line (or edge). Imagine a social network where each person is a point, and friendships are lines connecting them. An independent set would be a group of people with no direct friendships among them. These sets help mathematicians understand the structure of networks by identifying groups that are mutually non-interacting or unrelated within the context of the connections.