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Is their any Twitter API that can be accessed without authentication for - 1.) post by user and users Followers that are being Tweeted/re-twitted the most and 2.) users tweets that users followers have clicked on or re-twitted the most

Any kind of help will be appreciated.

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1 Answers

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According the the API v1 docs, this is possible, by including result_type=popular in the query string of your request.

For example, if you wanted to search for popular tweets relating to the search term popular tweets, your request would be as follows:

http://search.twitter.com/search.json?q=popular%20tweets&result_type=popular