IsAcyclic returns true if the input has no directed cycle and false otherwise.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{IsAcyclic}\left(\mathrm{Digraph}\left(\mathrm{Trail}\left(1\,2\,3\,4\,5\right)\right)\right)$

$\mathrm{true}$

$\mathrm{IsAcyclic}\left(\mathrm{Digraph}\left(\mathrm{Trail}\left(1\,2\,3\,4\,5\,2\right)\right)\right)$

$\mathrm{false}$