Facebook allows you to view and delete search history from Activity Log section. Facebook Search History contains every single search you performed using the Search box or Graph search (if enabled) in your account. So for privacy reasons, you may need to delete this from your activity logs at times. You should also know, that deleting any updates, photos or logs from facebook is a temporary action performed at your end but not a permanent action. Facebook stores any data you enter permanently or for long time. I have spotted this when i entered and remove my credit card from facebook account. You can find this article here “Facebook never removes credit card permanently“.
Many have got Facebook Graph Search enabled to their account and some users yet to get a graph search. If you have not joined facebook graph search waiting list, then visit the official page here and join in the waiting list.