PageRank is one of the first algorithms used by Google to determine webpage relevance, based on the quantity and quality of hyperlinks that refer to it. PageRank Data is no longer available for webmasters to see, but an advanced version of this algorithm is most likely still used by Google.
PageRank is one of the algorithms used in Google Search, in order to rank pages based on their overall domain authority and page authority. Although this is not the only algorithm used by Google, it is believed to still hold a great deal of relevance in the way rankings are decided. PageRank is based on link analysis and it takes into account the quantity and the quality of the backlinks that a webpage has. In this system, a hyperlink counts as a vote of support that automatically increases PageRank. If that vote comes from a website which has a high PR as well, it is considered a lot more valuable than a hyperlink from a source with low PageRank.
A version of the algorithm is most likely still part of the larger Google algorithm, but PageRank does not function in a vacuum. Since the algorithm can easily be manipulated (for example through link farms, spoofed redirects or other black hat techniques), it has to be doubled by other measures for relevance. For instance, Google most likely uses a version of TrustRank, to be able to separate Spam webpages from trustworthy websites. Other algorithms include Hummingbird, which determines relevance by looking for natural language queries and understanding context.
Versions of PageRank are also being used by other companies outside Google, as the mathematical model behind it has recently become public and the patent has expired, making it part of the public domain. Twitter uses a type of PageRank to show suggested profiles to its users. PageRank may also still be used for URL ordering during crawling. Since there are so many URLs and they are constantly changing, the bots need a criteria by which to establish the order in which to crawl them. PageRank is one such indicator.
However, PageRank data is no longer publicly displayed in Google Webmaster Tools and the Google Toolbar.