I think that the reason to anticoagulate someone is based upon a lot of criteria.Things such as a patient's medical history, the extent of surgery, and surgeon preference to name a few are included. I would say most do not need anticoagulation.
Generally in a healthy, active patient who does not have any prior history of clotting (leg blood clots, multiple unexplained miscarriages, etc), post operative anticoagulation is not required/needed. I do tend to use a preoperative dose of heparin (blood thinner) on the day of surgery and encourage early and frequent ambulation post operatively. We generally leave compression hose on our patients post operatively as well. Each surgeon has their own preference, so you should discuss with your plastic surgeon.