In the language of the Lovász Local Lemma, a dependency graph $G$ is one in which
- each $i$ vertex corresponds to an event $A_i$ and
- each event $A_i$ is mutually independent of the collection $\{A_j \mid ij \notin E(G), i \neq j\}$.
In words, each event is mutually independent of the collection of its non-neighbors in the dependency graph.
A dependency digraph is defined similarly, except the edges are directed.
Is there a simple example of events that define a dependency digraph that is not a dependency graph?
An example of such a thing would be events $A_1$, $A_2$, and $A_3$ for which $A_1$ is mutually independent of $\{A_2, A_3\}$, but $A_2$ is not mutually independent of $\{A_1, A_3\}$.