In the mathematical field of graph theory a complete graph is a simple graph where an edge connects every pair of vertices. 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. A planar graph cannot contain K5 (or the complete bipartite graph K3,3) as a minor.
Complete graphs on n vertices, for n between 1 and 8, are shown below: