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1) If an article is retweeted or referenced much in Twitter, do you count that as a signal outside of finding any non-nofollowed links that may naturally result from it?
Yes, we do use it as a signal. It is used as a signal in our organic and news rankings...
3) Do you calculate whether a link should carry more weight depending on the person who tweets it?
Yes we do use this as a signal, especially in the "Top links" section [of Google Realtime Search]. Author authority is independent of PageRank, but it is currently only used in limited situations in ordinary web search.