When is it safe to have sex or masturbate after hair transplant so that I do not lose the grafts or cause any damage?

If your surgery was on the scalp, you should be able to have sex after surgery.  Unless your version of sex involves the scalp area, use common sense and follow your doctors recommendations.

Hello, please see below for some helpful information. We advise to avoid sexual activity for first week after hair transplantation.  The rationale is to avoid increasing blood pressure.  There are no studies supporting this however.  
Best 
Anil Shah MD

72 hours is more than enough to have sex. On the other hand you should be careful about the recipient site and avoid any high physical pressure on the area.Anyway following up your doctor's advice is more important.

you can have sexual activity after the first night. You just have to make sure you do not touch the recipient area where the grafts are implanted. 

Within 48 hours, you can have sex after a hair transplant. The increased activity will not be a problem.