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Citation Flow and Trust Flow are two link authority metrics from Majestic SEO, a major provider of information and analytics about backlinks. They are intended to help characterize the quality and importance of backlinks, far better than what is possible using the extremely limited information released by Google directly.
Both metrics are offered on a scale of 0-100, which gives them greater granularity than either PageRank (which is known for being far from accurate and has been discontinued) or ACRank. Also, they are updated daily based on Majestic SEO's Fresh index data. The combination of a more granular scale and daily (rather than quarterly) updates make them better metrics for studying a site - either yours, or your competitors'.
Citation Flow is in many ways similar to the old PageRank score from Google, in that it is a gauge of how many other pages link to your site, weighted by the relative strength of each site. In our previous tests, it is far more accurate than PageRank was.
Citation Flow replaces the AC Rank value which has been used in our SEO Competition module's anchor text analysis feature since the PR value became unreliable.
Trust Flow is a somewhat different measurement, which has more in common with Yahoo's old "Trust Rank" value or the Moz 'MozTrust' score. It begins with a large database of sites which are rated by human SEO experts, and the web of links which spread out from (and lead back to) these sites are evaluated based on the subjective judgements of these experts.
Since trustworthy sites tend to link to other trustworthy sites, this gives an indication of link quality which is entirely separate from the sheer quantity of links you may have. It's a bit like the "Six Degrees of Separation" game, if you're familiar with that; a site gains in Trust Flow by being closely linked to a site that is known to be trustworthy. The further away you are from high-status site - the longer the chain of links between you and the 'nearest' high-trust sites in the network of links - the lower your site's Trust Flow rating will be.
For more information on these metrics, Majestic SEO's glossary entry on Flow Metrics has a link to a 7-minute instructional video which also explains the CF/TF graphs you can get by clicking through from the SEO Competition results matrix.
Majestic SEO scans over a hundred billion pages and indexes them on a daily basis, performing calculations to update the insights on the network of links in its catalog. While even they cannot scan the web as thoroughly as Google does, they are by far the best source of information available to the general public and their results have stood up to our most careful testing.
You can also read about how Majestic data is used in our Keyword Research module in this article