A complete graph is a graph, which has edges connecting all pairs of vertices.

Essential Further Mathematics 4ed 2012 (page 624)

*In the above diagram, only K5 is a complete.

To work out the number of edges a complete graph will have, the vertices can be used to work that out using this formula:

$\frac {n(n-1)}{2}$

where ‘n’ is equal to the number of vertices.

In order to determine whether a graph is complete, from an adjacency matrix one key feature to look for in the matrix is a row of 0s in the diagonal, with 1s filling the rest of the matrix.

Essential Further Mathematics 4ed 2012 (page 624)