PageRank

"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.""

"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."

"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."

"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."

"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."