Digg is dying just when traffic from social media to web sites increases. Social traffic is becoming as important, or more so, than search traffic from the likes of Google (GOOG) and Yahoo (YHOO).

Gawker Media, one of the biggest publisher on the internet has seen it traffic from social sites increase from 10 million visits a month from social sites to 20 million year over year – of which Facebook accounts for 7.7 million visits or a third of the visits.

Less than a year ago, Digg was the single most important social site for Gawker. Now it has been eclipsed by the likes of Facebook. Reddit, Condé Nast’s “Digg clone,” is catching up as well.