Visual Explanation of Maximum Clique Maximum clique is a technique used to find the largest vertex cluster where each vertex is connected to each other. Let’s look at an example. We’ll examine each vertex and see what the greatest cluster of the following graph will be. Let’s look at the first vertex. Vertex 1 is connected to vertices 2, 4, and 6. We need to make sure that each of those vertices has a connection to one another as well. Is vertex 2 connected to vertex 4? Yes Is vertex 2 connected to vertex 6? Yes Is vertex 4 connected to