# complete graph

A complete graph is a connected graph in which exactly one
edge connects each pair of vertices.
A complete graph with *n* vertices, denoted *K*_{n},
has *n*(*n* - 1)/2 edges (i.e., the *n*th triangular
number), (*n*-1)! Hamilton
circuits, and a chromatic number of *n*. Every vertex in *K*_{n} has degree *n*-1;
therefore *K*_{n} has an Euler
circuit if and only if *n* is odd. In a **weighted complete
graph**, each edge has a number called a weight attached to it. Each
path then has a total weight, which is the sum of the weights of the edges
in the path.