Let $\sigma = (\sigma_0, ..., \sigma_{n-1})$ be a permutation on the natural numbers $0$ to $n - 1$. Then we define the directed graph $G(V, E)$ such that $V = (v_0, ..., v_{n-1})$ represents the elements of the permutation and $(v_i, v_j) \in E$ when $i < j$ and $\forall k \in \Bbb N, i < k < j$ it is true that $\sigma_k > max(\sigma_i, \sigma_j)$.
For example, if $\sigma = (4, 5, 2, 1, 3)$, then $E = \{ (v_0, v_1), (v_0, v_2), (v_1, v_2), (v_2, v_3), (v_3, v_4) \}$.
I came across this graph definition when playing around with methods for ranking a list of items. Googling for 'permutation graph' produced a graph definition (https://en.wikipedia.org/wiki/Permutation_graph), but this definition generates completely different graphs for the same input permutation. Does my definition - or some analogy of it - exist under a name I don't know?
The reason I want to know is to learn more about this kind of graph, and perhaps use some of its properties for improving the ranking algorithms I'm working on.