Do you know Graph theory?

first of all what is complete graph: A complete digraph is a directed graph in which every pair of distinct vertices is connected by a pair of unique edges

how to calculate number of edges in complete graph: The complete graph on n vertices is denoted by $K_n$ which has $\frac{n(n - 1)}{2}$ edges

now just put $n=8$ which gives number of edges equal to $\boxed{28}$

To count the number of edges in a complete graph $K_n$ , we can think how many pairs of vertices we have in $K_n$ . We know there is a edge between every pair of vertices. So, for $n$ this is:

$\dbinom{n}{2}$

Then, for $n=8$ :

$\dbinom{8}{2}=\boxed{28}$