A unipathic graph is a directed graph such that there is at most one simple path from any one vertex to any other vertex.
Unipathic graphs can have cycles. For example, a doubly linked list (not a circular one!) is a unipathic graph; if the list has $n$ elements, the graph has $n-1$ cycles of length 2, for a total of $2(n-1)$.
What is the maximum number of edges in a unipathic graph with $n$ vertices? An asymptotic bound would do (e.g. $O(n)$ or $\Theta(n^2)$).
Inspired by Find shortest paths in a weighed unipathic graph; in my proof, I initially wanted to claim that the number of edges was $O(n)$ but then realized that bounding the number of cycles was sufficient.