PageRank
PageRank is a computational method that derives the importance of a web page from how many other pages link to it. It was the founding idea behind Google Search and continues to shape how rankings in networks are calculated to this day.
On the internet, pages refer to one another through links. A link is a clickable reference that leads from one page to another. PageRank is a computational method that calculates a number for each page from this web of references. This number is meant to express how important a page is within the overall network. The underlying assumption is simple: whoever is linked to often is presumably significant. The method was developed in 1996 by Larry Page and Sergey Brin at Stanford University. It became the foundation of the Google search engine.
Why links reveal more than words
Early search engines ranked results mainly by how often a search term appeared on a page. This was easy to exploit. Anyone who invisibly wrote the word “vacation” a hundred times on their page ended up near the top. The results lists were correspondingly useless.
PageRank reversed this perspective. It is not the page operator who decides on their own importance, but the rest of the network. A link functions like a recommendation in this respect. Such recommendations are harder to fake than one’s own text, because they come from external servers.
The result was a noticeable leap in quality. From 1998 onward, Google displaced the established competitors with this approach. However, the idea extends far beyond search engines: wherever things refer to one another, similar calculations can be applied. Examples include scientific papers that cite one another, or user accounts in social networks.
The random surfer and the calculation loop
The method can be described as a thought experiment. Imagine someone clicking aimlessly around the web. They start on some page and always follow a random link. The PageRank of a page is the probability that this surfer is on it at any given moment.
Crucially, not all links count equally. A recommendation from an important page carries more weight than one from an unknown page. Furthermore, a page’s value is divided among its outgoing links. A page with three links passes on more value per link than a page with three hundred links. This makes the calculation circular: the importance of a page depends on the importance of other pages.
This is resolved through repetition. All pages are initially given the same starting value, and the distribution is recalculated over and over again. After a few dozen iterations, the numbers barely change anymore, and the result becomes stable. An additional mechanism prevents dead ends: with a probability of about 15 percent, the surfer jumps to a completely random page. Without this jump, groups of pages with no outgoing links would collect the entire value.
PageRank today: search engines, citations, networks
In Google Search, PageRank has long been just one factor among hundreds. Today, content, freshness, the user’s location, and language models that understand the substance of search queries are more important. The PageRank indicator that was once publicly visible in the Google Toolbar was discontinued in 2016. A common misconception is therefore that PageRank is equivalent to a page’s position in the search results. It is only one component of that.
In search engine optimization, or SEO for short, the principle still plays a role nonetheless. Companies try to obtain links from reputable pages. This is precisely why a market for purchased links emerged, one that search engines have been combating for years.
Outside the web, the method is firmly established. Libraries use it to evaluate the influence of academic papers, biologists use it to rank proteins in metabolic networks, and banks look for suspicious patterns in chains of transfers. Anyone reading news about recommendation systems or network analysis often encounters variants of this idea.