Table[
SeedRandom[i];
gr = RandomGraph[{20000, 30000}, DirectedEdges -> True];
If[FindCycle[gr] === $Aborted[], i, 0]
, {i, 1, 100}]
SeedRandom[1]
gr = RandomGraph[{15600, 20700}, DirectedEdges -> True];
FindCycle[gr]
SeedRandom[1]
gr = RandomGraph[{115600, 120700}, DirectedEdges -> True];
FindCycle[gr]