The researchers suspect that beards indicate social dominance and may be more strongly preferred for long-term relationships. They also found that beards can help mask 'overly feminine or masculine traits' in a face, so can increase attractiveness.
They also found that “light and heavy stubble faces were more attractive than either full beards and clean-shaven faces.”
But there's still more research to be done - they're keen to investigate how social and cultural dynamics affect what kinds of beard shapes are most attractive. And can we say, we're all for this study!