Looking at the Blue Flame popularity number is a great way to quickly judge the popularity of pins in your Communities. You can find it by looking at the top right corner of a Pin in a Community.

The Blue Flame count updates usually every 24 hours, and counts the number of times the exact source URL for that Pin appears on social networks. This generally matches the number of shares you'd see in a blog social share counter (like Social Warfare).
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There can be a difference in the Blue Flame count vs other methods - as we only count URLs which match that Pin exactly. Meaning if anyone else shares the same source, but includes something like their own Google Analytics tracking code as an example (eg: a UTM code at the end of the link), this will be seen as a different URL and not be included in our tracking. Whereas this may be included in other methods you're using to determine the number of shares.
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Want to know more about how the Blue Flame number is calculated? Check out our Knowledge Base article: What does the Blue Flame represent on my Community's Pins?