Consider the following two methods for generating a random graph: 1. start from an empty graph. randomly add edges until you form a triangle. undo the final added edge, and then halt. 2. start from the complete graph. randomly delete edges until you become triangle free and then halt.
Now, a priori these kind of seem like different things. It turns out they generate the same graphs with the same probabilities.
Proof. rather than thinking about choosing edges one at a time just number them all up front. then, you can think about going forwards or backwards in a list of all the edges. there is a unique threshold thing when you go from triangle free to having triangles. the two different methods meet in this middle point.