In a study by Pelphrey et al., 2002 the authors show that when people are asked to scan a face, they spend about 80% of the time looking at the eyes, about 10% on the nose region, and a few percents on the mouth (the remaining few percentages were spent on other non-core features such as ears, forehead etc). Hence, the eyes by far draw the most attention and represent the most important feature when it comes to facial processing.
A typical example of a visual scan by a human subject as examined by eye tracking is the following (taken from Pelphrey et al., 2002), which shows that the subject scanned the core features of the facial image (eyes, nose, mouth):
Nonetheless, the presence of a complete face makes recognition more efficient than when looking at incomplete faces (Tanaka & Farah, 1993)