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Social Shares uses the Facebook and Twitter APIs to fetch the total number of shares for each of your posts. The number of shares is stored in your database for any plugins to use. Social Shares can optionally display the number of shares on your posts. The number of shares is styleable. You can use the shortcode [social_shares] anywhere in your posts.
In addition, you can sort your posts by the number of shares. You can make a page that displays your posts with the most shares. Simply add ?sort_shares=desc or ?sort_shares=asc to the end of any WordPress URL to sort by the number of shares.
Screenshots
Options page.