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How does Twitter, or how can Twitter, benefit Page Rank?
Get as many links as possible - from different profiles. Do SEO on it too like you would any website.
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This is a Google related topic not a marketing topic - moved to Google category.
Twitter links are no follow so wont pass any PR juice anyway. But it's still link like any other but from Twitter which is a high authority site in itself. The PR of the homepage was a PR9 I think on last check when checks showed but that doesn't mean the tweet page is a PR9. That would be a PR0 and not pass the same amount of juice to it. Unless it was on the homepage for a while but it wouldn't be long on it buried under millions of other tweets. But as said it is no follow anyway so none would anyway. It's do follow links that pass rank juice through, or rather, no no follow links as there's no such thing as a do follow tag! It's automatically do follow unless a no follow tag is specified.
If what you mean is for the Page Rank to benefit from Twitter then you are in effect taking about the ranking of the site in the search engines particularly Google. Twitter is a social media that you can use your account to promote your site. The tweets about your site that contains the link can be considered backlinks that can boost the ranking of you site in the search engines. The Page Rank, by the way, is not being used anymore by Google so we might as well forget all about it.
In the PRSA’s Public Relations Journal, Angelica , Jane and Scott examine the importance of the microblogging web site in their contents, Twitter as a Public Relations Tool. The three authors interviewed a dozens of executive-level PR professionals to work out the worth of Twitter as a part of a social media strategy. I highly suggest that anyone with an interest in Twitter and PR browse this text.