Answer :
const TopoDS_Edge &edg(TopoDS::Edge(edgeExplorer.Current()));
TopTools_ListOfShape parents;
parents = edgeAnceMap.FindFromKey(edg);
const TopoDS_Shape& face1 = parents.First();
const TopoDS_Shape& face2 = parents.Last();
GeomAbs_Shape cont = BRep_Tool::Continuity(edg, TopoDS::Face(face1), TopoDS::Face(face2));
if (cont == 0)
{ // Sharp edge
std::cout << "Sharp edge" << std::endl;
}
else
{ // Dead edge
std::cout << "Unsharp edge" << std::endl;
}