In the mathematical fiel of graph theory, a complete graph is a simple graph in which every pair of distinct vertices is connected by an edge. The complete graph on n vertices has n vertices and n(n − 1) / 2 edges, and is denoted by Kn. It is a regular graph of degree n − 1. All complete graphs are their own cliques. They are maximally connected as the only vertex cut which disconnects the graph is the complete set of vertices.