  Given a finite group $G$, the Engel graph of $G$ is a directed graph encoding
pairs of elements satisfying some Engel word. From the work of Detomi, Lucchini
and Nemmi, the strongly connectivity of the Engel graph of an arbitrary group
$G$ is reduced to the understanding of the strongly connectivity of the Engel
graph of non-abelian simple groups.
  In this paper, we investigate the strongly connectivity of the Engel graph of
finite non-abelian simple groups.
