Suppose you are given a sparse directed graph on $n$ vertices with a maximum degree at most $d$ and a parameter $\epsilon \in [0,1]$. We wish to design a testing algorithm that accepts (with probability 2/3) when the digraph is acyclic and rejects (with probability 2/3) when at least $\Omega(\epsilon n d)$ edges need to be removed to make the digraph acyclic. The algorithm can access the digraph by querying a vertex and getting back a list of outgoing and incoming edges from said vertex.
Does there exist a tester that makes $o_{\epsilon, d}(n)$ queries?