To delete parts form the storage, query the structure to be deleted uniquely and call the Delete method.
To delete the film Inception from the graph:
Define the structure to be deleted. Query it. Optionally check that the Status is QueriedUniqueHit. We know it is here though. Finally execute the Delete command.
var filmToDelete = new Part("Film").Add(new Part("Title").Add(new Simple<string>("Inception")));
nest.Query(filmToDelete);
nest.Delete(filmToDelete);
This is what remains after the delete:

Note that the loose ends Year and Director are removed as well - although not specifically defined in the Delete structure.