christmas combinatorics

assuming everyone knows how the 'secret santa' system works

given n people in a randomly selected 'secret santa' arrangement (each person draws a name out of a hat, nobody can have themself, etc), what is the probability that there are no pairs of people that have each other?

this question has been bugging the hell out of me because i don't know enough graph theory and it can probably be solved with digraphs. plus it's probably obvious

How exactly were you going to approach it with graph theory?