  In prior work, Cho and Kim studied competition graphs arising from doubly
partial orders. In this article, we consider a related problem where
competition graphs are instead induced by permutations. We first show that this
approach produces the same class of competition graphs as the doubly partial
order. In addition, we observe that the $123$ and $132$ patterns in a
permutation induce the edges in the associated competition graph. We classify
the competition graphs arising from $132$-avoiding permutations and show that
those graphs must avoid an induced path graph of length 3. Finally, we consider
the weighted competition graph of permutations and give some initial
enumerative and structural results in that setting.
