# PageRank

PageRank (PR) is an algorithm used by Google's search engine to rank web pages. The algorithm's name derives from the term "web page" and also Larry Page, who co-founded the Google company with Sergey Brin.

## Quotes

* A major reason Google’s search engine is so successful is its PageRank algorithm, which assigns a pecking order to Web pages based on the pages that point to them. A page is important, according to Google, if other important pages link to it. But the Internet is not the only web around. In ecology, for instance, there are food webs — the often complex networks of who eats whom. Inspired by PageRank, Stefano Allesina of the University of Chicago and Mercedes Pascual of the University of Michigan have devised an algorithm of their own for the relationships in a food web. As described in the online open-access journal PLoS Computational Biology, the algorithm uses the links between species in a food web to determine the relative importance of species in a food web, which will have the most impact if they become extinct. ... One key to PageRank’s success is that its developers introduced a small probability that a Web user would jump from one page to any other. This in effect makes the Web circular, and makes the algorithm solvable. But in food webs, Dr. Allesina said, “you can’t go from the grass to the lion — the grass has to go through the gazelle first."
** Henry Fountain, (September 4, 2009)"Googling a Worldwide Food Web of Extinction". The New York Times.
* PageRank is a well-known algorithm for measuring centrality in networks. It was originally proposed by Google for ranking pages in the World Wide Web. One of the intriguing empirical properties of PageRank is the so-called ‘power-law hypothesis’: in a scale-free network, the PageRank scores follow a power law with the same exponent as the (in-)degrees. To date, this hypothesis has been confirmed empirically and in several specific random graphs models.
** Alessandro Garavaglia, Remco van der Hofstad, and Nelly Litvak, (2020). "Local weak convergence for PageRank". The Annals of Applied Probability 30 (1): 40-79.
… Amit Singhal and hundreds of other Google engineers are constantly tweaking the company’s search engine in an elusive quest to close the gap between often and always. Mr. Singhal is the master of what Google calls its “ranking algorithm” — the formulas that decide which Web pages best answer each user’s question. It is a crucial part of Google’s inner sanctum, a department called “search quality” that the company treats like a state secret. Google rarely allows outsiders to visit the unit, and it has been cautious about allowing Mr. Singhal to speak with the news media about the magical, mathematical brew inside the millions of black boxes that power its search engine. … Google does more than simply build an outsized, digital table of contents for the Web. Instead, it actually makes a copy of the entire Internet — every word on every page — that it stores in each of its huge customized data centers so it can comb through the information faster. Google recently developed a new system that can hold far more data and search through it far faster than the company could before. As Google compiles its index, it calculates a number it calls PageRank for each page it finds. This was the key invention of Google’s founders, Mr. Page and Sergey Brin. PageRank tallies how many times other sites link to a given page. Sites that are more popular, especially with sites that have high PageRanks themselves, are considered likely to be of higher quality. Mr. Singhal has developed a far more elaborate system for ranking pages, which involves more than 200 types of information, or what Google calls “signals.” PageRank is but one signal. Some signals are on Web pages — like words, links, images and so on. Some are drawn from the history of how pages have changed over time. Some signals are data patterns uncovered in the trillions of searches that Google has handled over the years.
** Saul Hansell, (June 3, 2007)"Google Keeps Tweaking Its Search Engine". The New York Times.
* PageRank (the name is a trademark of Google) is a method of measuring the popularity or importance of web pages. PageRank is a mathematical algorithm, or systematic procedure, at the heart of Google's search software.
** Peter Lynch, That's Maths: The Mathematical Magic in Everyday Life. Gill & Macmillan (2016).
* The importance of a Web page is an inherently subjective matter, which depends on the readers interests, knowledge and attitudes. But there is still much that can be said objectively about the relative importance of Web pages. This paper describes PageRank, a method for objectively and mechanically rating, effectively measuring the human interest and attention devoted to them. We compare PageRank to an idealized random Web surfer. We show how to efficiently compute PageRank for large numbers of pages. And we show how to apply PageRank to search and to user navigation.
** Larry Page, The PageRank Citation Ranking: Bringing Order to the Web. stanford.edu (January 29, 1998).
* One of the major breakthroughs with Google’s search engine was a formula called PageRank, named after Larry Page, one of Google’s founders and now the chief executive of its parent company, Alphabet. PageRank works on the basic premise that a page’s value can be determined by how many sites link to it. In the early days of web search, this was a novel concept, and it helped to propel Google past competitors like Yahoo and AltaVista. The search engine has gotten more sophisticated over the years. (It was founded 20 years ago on Tuesday.) In addition to PageRank, the company has also said that the software looks at how often and where the keywords being searched for show up on a specific page, how recently the page was created (a sign of the freshness of the information) and the location of the person making the search.
** Daisuke Wakabayashi, (September 5, 2018)"Trump Says Google Is Rigged, Despite Its Denials. What Do We Know About How It Works?". The New York Times.

## External links

* Encyclopedic article on PageRank on Wikipedia
* The dictionary definition of pagerank on Wiktionary