Ways of measuring link popularity
The search engines have different ways of determining the popularity of a page. Most of these are based on the number of links to a page. Generally, the more links to a page the more popular it is and the higher it could rank. However, in recent years the search engines have become more sophisticated and the link juice passed by each link is not equal. Some links pass more benefit than others. It is assume that the easily gained self promotional links carry less weight and the harder gained editorially gained links carry more weight.
Google has it Pagerank (PR) score that it gives each page which is supposed to represent the link popularity of a page. The problem with PR is that, while they update it daily internally, they only export it every 3 or so months for us to look at, so its old data. The PR also a global link score and does not indicate the strength or link juice of the links that make up the PR. Google also penalise sites and artificially manipulate the visible PR, so it cannot be considered that reliable for many sites.
Then we have Bing’s Page Score, which is a score that Bing give a page. But it is not entirely clear what it is that makes up the score and Bing have not been very forthcoming.
Outside the search engines, SEOMOZ have introduced mozRank and mozTrust and use their Linkscape database to calculate the metrics. The mozRank, which is similar to Google PR, but is not affected by the penalties and artificial manipulation that Google do, so can give you a different picture. The mozTrust which is a measure of the authority of a web site. Links from authority pages are the most sort after, so this is also a useful measure to understand.