A hard bump on the face that is purple may be purple because of a deep infection, or a soft tissue infection deep in the skin. Because of the infection, there is localized inflammatory edema, which may be hard to the touch, so it is a hard bump that is purple. Of course, in addition to this case, there may also be subcutaneous cysts or epidermoid cysts on the face, because epidermoid cysts may also appear as hard bumps, and once there is an infection, hard bumps will appear, and purple, with a certain degree of pain, and there are redness and swelling in the surrounding symptoms. Of course, there is also the possibility of localized subcutaneous hemorrhage, which can also appear hard and purple.