Maximum Edges in a Simple Graph

In a simple graph, at most one edge can connect any given pair of vertices.

Count the number of distinct unordered pairs of vertices.

1. 1. Count vertex pairs

   A simple undirected graph can have at most one edge per unordered pair of distinct vertices.

2. 2. Apply the combination count

   The number of unordered pairs from $n$ vertices is $\left(\genfrac{}{}{0ex}{}{n}{2}\right)$, which equals the maximum edge count.

   $$\left(\genfrac{}{}{0ex}{}{n}{2}\right)=\frac{n(n-1)}{2}$$

Answer: n(n-1)/2