Complete Graph

We have a theorem that states that the number of edges in any $K_{n}= (\frac{1}{2}$ ) $(n)((n-1)$ = $\frac{1}{2}$ $1000$ $\times$ $900$ = $499,500$ ; where $n \text{ is the number of vertices}$ .

Also, by looking at the graphs, you can deduce this formula. Let $e= edges$

Notice, when $n=7 \implies e=21$

when $n=6 \implies e =15$ and

when $n=5 \implies e=10$ , by counting the number of edges from the graph. Make sure you don't count the same edge twice.