PageRank is a link analysis Network theory is an area of computer science and network science and part of graph theory. It has application in many disciplines including particle physics, computer science, biology, economics, operations research, and sociology. Network theory concerns itself with the study of graphs as a representation of either symmetric relations or, more algorithm, named after Larry Page Lawrence "Larry" Page is the American co-founder of Google Inc., along with Sergey Brin. They are often known together as the "Google Guys". According to Forbes he is currently the 24th richest person in the world with a personal wealth of US$17.5 billion in 2010,^[1] used by the Google Google Inc. is a multinational public cloud computing, Internet search, and advertising technologies corporation. Google hosts and develops a number of Internet-based services and products, and generates profit primarily from advertising through its AdWords program. The company was founded by Larry Page and Sergey Brin, often dubbed the " Internet search engine A web search engine is designed to search for information on the World Wide Web. The search results are generally presented in a list of results and are often called hits. The information may consist of web pages, images, information and other types of files. Some search engines also mine data available in databases or open directories. Unlike Web that assigns a numerical weighting to each element of a hyperlinked In computing, a hyperlink is a reference to a document that the reader can directly follow, or that is followed automatically[citation needed]. The reference points to a whole document or to a specific element within a document. Hypertext is text with hyperlinks. Such text is usually viewed with a computer. A software system for viewing and set In computer science, a set is an abstract data structure that can store certain values, without any particular order, and no repeated values. It is a computer implementation of the mathematical concept of a finite set of documents, such as the World Wide Web The World Wide Web, abbreviated as WWW and commonly known as the Web, is a system of interlinked hypertext documents accessed via the Internet. With a web browser, one can view web pages that may contain text, images, videos, and other multimedia and navigate between them by using hyperlinks. Using concepts from earlier hypertext systems, British, with the purpose of "measuring" its relative importance within the set. The algorithm In mathematics, computer science, and related subjects, an 'algorithm' is an effective method for solving a problem expressed as a finite sequence of instructions. Algorithms are used for calculation, data processing, and many other fields may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).

The name "PageRank" is a trademark A trademark or trade mark is a distinctive sign or indicator used by an individual, business organization, or other legal entity to identify that the products or services to consumers with which the trademark appears originate from a unique source, and to distinguish its products or services from those of other entities of Google, and the PageRank process has been patented A patent is a set of exclusive rights granted by a state (national government) to an inventor or their assignee for a limited period of time in exchange for a public disclosure of an invention (U.S. Patent 6,285,999). However, the patent is assigned to Stanford University The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university located in Stanford, California, United States. The university was founded in 1891 by the Californian railroad tycoon Leland Stanford and named for his recently deceased son. Its alumni have founded the companies Hewlett- and not to Google. Google has exclusive license rights on the patent from Stanford University. The university received 1.8 million shares of Google in exchange for use of the patent; the shares were sold in 2005 for $ The United States dollar is the official currency of the United States. The U.S. dollar is normally abbreviated as the dollar sign, $, or as USD or US$ to distinguish it from other dollar-denominated currencies and from others that use the $ symbol. It is divided into 100 cents336 million.^[2][3]

Description

Google describes PageRank:^[4]

In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively Recursion, in mathematics and computer science, is a method of defining functions in which the function being defined is applied within its own definition; specifically it is defining an infinite statement using finite components. The term is also used more generally to describe a process of repeating objects in a self-similar way. For instance, and depends on the number and PageRank metric of all pages that link to it ("incoming links"). A page that is linked to by many pages with high PageRank receives a high rank itself. If there are no links to a web page there is no support for that page.

Google assigns a numeric weighting from 0-10 (but 0 is used just for penalized or non analyzed-pages) for each webpage on the Internet; this PageRank denotes a site’s importance in the eyes of Google. The PageRank is derived from a theoretical probability value on a logarithmic scale A logarithmic scale is a scale of measurement that uses the logarithm of a physical quantity instead of the quantity itself like the Richter Scale The Richter magnitude scale, also known as the local magnitude scale, assigns a single number to quantify the amount of seismic energy released by an earthquake. It is a base-10 logarithmic scale obtained by calculating the logarithm of the combined horizontal amplitude (shaking amplitude) of the largest displacement from zero on a particular type. The PageRank of a particular page is roughly based upon the quantity of inbound links as well as the PageRank of the pages providing the links. It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar Google Toolbar is an Internet browser toolbar available for Internet Explorer and Mozilla Firefox also influence the PageRank.^{[citation needed]} In order to prevent manipulation, spoofing In the context of network security, a spoofing attack is a situation in which one person or program successfully masquerades as another by falsifying data and thereby gaining an illegitimate advantage and Spamdexing Spamdexing involves a number of methods, such as repeating unrelated phrases, to manipulate the relevancy or prominence of resources indexed by a search engine, in a manner inconsistent with the purpose of the indexing system. Some consider it to be a part of search engine optimization, though there are many search engine optimization methods that, Google provides no specific details about how other factors influence PageRank.^{[citation needed]}

Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.^[5] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank.

Other link-based ranking algorithms for Web pages include the HITS algorithm Hyperlink-Induced Topic Search (also known as Hubs and authorities) is a link analysis algorithm that rates Web pages, developed by Jon Kleinberg. It determines two values for a page: its authority, which estimates the value of the content of the page, and its hub value, which estimates the value of its links to other pages invented by Jon Kleinberg Jon Michael Kleinberg is an American computer scientist, MacArthur Fellow, Nevanlinna Prize winner, and the Tisch University Professor of Computer Science at Cornell University (used by Teoma Teoma, pronounced chawmuh , was an Internet search engine founded in 2000 by Professor Apostolos Gerasoulis and his colleagues at Rutgers University in New Jersey. Professor Tao Yang from the University of California, Santa Barbara co-led technology R&D. Their research grew out of the 1998 DiscoWeb project. The original research was published and now Ask.com Ask is a search engine founded in 1996 by Garrett Gruener and David Warthen in Berkeley, California. The original search engine software was implemented by Gary Chevsky from his own design. Chevsky, Justin Grant, and others built the early AskJeeves.com website around that core engine. Three venture capital firms, Highland Capital Partners,), the IBM CLEVER project, and the TrustRank TrustRank is a link analysis technique described in a paper by Stanford University and Yahoo! researchers for semi-automatically separating useful webpages from spam algorithm.

History

PageRank was developed at Stanford University The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university located in Stanford, California, United States. The university was founded in 1891 by the Californian railroad tycoon Leland Stanford and named for his recently deceased son. Its alumni have founded the companies Hewlett- by Larry Page Lawrence "Larry" Page is the American co-founder of Google Inc., along with Sergey Brin. They are often known together as the "Google Guys". According to Forbes he is currently the 24th richest person in the world with a personal wealth of US$17.5 billion in 2010 (hence the name Page-Rank^[6]) and later Sergey Brin Sergey Brin is a Russian-American computer scientist, who, along with Larry Page, is best known as the co-founder of Google, Inc., the world’s largest Internet company , based on its search engine and online advertising technology. Together with Page, they are often referred to as the "Google Guys". According to Forbes he is currently as part of a research project about a new kind of search engine. It was co-authored by Rajeev Motwani and Terry Winograd. The first paper about the project, describing PageRank and the initial prototype of the Google search Google Search or Google Web Search is a web search engine owned by Google Inc. and is the most-used search engine on the Web. Google receives several hundred million queries each day through its various services. The main purpose of Google Search is to hunt for text in webpages, as opposed to other data, such as with Google Image Search. Google engine, was published in 1998^[5]: shortly after, Page and Brin founded Google Inc. Google Inc. is an American public corporation, earning revenue from advertising related to its Internet search, e-mail, online mapping, office productivity, social networking, and video sharing services as well as selling advertising-free versions of the same technologies. Google has also developed an open source web browser and a mobile operating, the company behind the Google search engine. While just one of many factors which determine the ranking of Google search results, PageRank continues to provide the basis for all of Google's web search tools.^[4]

PageRank has been influenced by citation analysis Citation analysis is the examination of the frequency, patterns and graphs of citations in articles and books. It uses citations in scholarly works to establish links to other works or other researchers. It is one of the most widely used methods of bibliometrics. Automated citation analysis and indexing has changed the nature of the research, early developed by Eugene Garfield Eugene "Gene" Garfield is an American scientist, one of the founders of bibliometrics and scientometrics. He received a PhD in Structural Linguistics from the University of Pennsylvania in 1961. Dr. Garfield was the founder of the Institute for Scientific Information (ISI), which was located in Philadelphia, Pennsylvania. ISI now forms a in the 1950s at the University of Pennsylvania, and by Hyper Search Hyper Search has been the first published technique to introduce link analysis for search engines, opening the way for the second-generation of search engines, developed by Massimo Marchiori at the University of Padua. In the same year PageRank was introduced (1998), Jon Kleinberg Jon Michael Kleinberg is an American computer scientist, MacArthur Fellow, Nevanlinna Prize winner, and the Tisch University Professor of Computer Science at Cornell University published his important work on HITS Hyperlink-Induced Topic Search (also known as Hubs and authorities) is a link analysis algorithm that rates Web pages, developed by Jon Kleinberg. It determines two values for a page: its authority, which estimates the value of the content of the page, and its hub value, which estimates the value of its links to other pages. Google's founders cite Garfield, Marchiori, and Kleinberg in their original paper.^[5]

Algorithm

PageRank is a probability distribution In probability theory and statistics, a probability distribution identifies either the probability of each value of a random variable , or the probability of the value falling within a particular interval (when the variable is continuous). The probability distribution describes the range of possible values that a random variable can attain and the used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. PageRank can be calculated for collections of documents of any size. It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.

A probability is expressed as a numeric value between 0 and 1. A 0.5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.

Simplified algorithm

Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.

In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the formulas below) would assume a probability distribution between 0 and 1. Here a simple probability distribution will be used- hence the initial value of 0.25.

If pages B, C, and D each only link to A, they would each confer 0.25 PageRank to A. All PageRank PR( ) in this simplistic system would thus gather to A because all links would be pointing to A.

This is 0.75.

Suppose that page B has a link to page C as well as to page A, while page D has links to all three pages. The value of the link-votes is divided among all the outbound links on a page. Thus, page B gives a vote worth 0.125 to page A and a vote worth 0.125 to page C. Only one third of D's PageRank is counted for A's PageRank (approximately 0.083).

In other words, the PageRank conferred by an outbound link is equal to the document's own PageRank score divided by the normalized number of outbound links L( ) (it is assumed that links to specific URLs only count once per document).

In the general case, the PageRank value for any page u can be expressed as:

,

i.e. the PageRank value for a page u is dependent on the PageRank values for each page v out of the set B_u (this set contains all pages linking to page u), divided by the number L(v) of links from page v.

Damping factor

The PageRank theory holds that even an imaginary surfer who is randomly clicking on links will eventually stop clicking. The probability, at any step, that the person will continue is a damping factor d. Various studies have tested different damping factors, but it is generally assumed that the damping factor will be set around 0.85.^[5]

The damping factor is subtracted from 1 (and in some variations of the algorithm, the result is divided by the number of documents (N) in the collection) and this term is then added to the product of the damping factor and the sum of the incoming PageRank scores. That is,

So any page's PageRank is derived in large part from the PageRanks of other pages. The damping factor adjusts the derived value downward. The original paper, however, gave the following formula, which has led to some confusion:

The difference between them is that the PageRank values in the first formula sum to one, while in the second formula each PageRank gets multiplied by N and the sum becomes N. A statement in Page and Brin's paper that "the sum of all PageRanks is one"^[5] and claims by other Google employees^[7] support the first variant of the formula above.

Google recalculates PageRank scores each time it crawls the Web and rebuilds its index. As Google increases the number of documents in its collection, the initial approximation of PageRank decreases for all documents.

The formula uses a model of a random surfer who gets bored after several clicks and switches to a random page. The PageRank value of a page reflects the chance that the random surfer will land on that page by clicking on a link. It can be understood as a Markov chain A Markov chain is a discrete random process with the property that the next state depends only on the current state. It is named for Andrey Markov, and is a mathematical tool for statistical modeling in modern applied mathematics, particularly information sciences. A useful heuristic is that of a frog jumping among several lily-pads, where the in which the states are pages, and the transitions are all equally probable and are the links between pages.

If a page has no links to other pages, it becomes a sink and therefore terminates the random surfing process. If the random surfer arrives at a sink page, it picks another URL In computing, a Uniform Resource Locator is a Uniform Resource Identifier (URI) that specifies where an identified resource is available and the mechanism for retrieving it. In popular usage and in many technical documents and verbal discussions it is often incorrectly used as a synonym for URI,. The best-known example of a URL is the " at random and continues surfing again.

When calculating PageRank, pages with no outbound links are assumed to link out to all other pages in the collection. Their PageRank scores are therefore divided evenly among all other pages. In other words, to be fair with pages that are not sinks, these random transitions are added to all nodes in the Web, with a residual probability of usually d = 0.85, estimated from the frequency that an average surfer uses his or her browser's bookmark feature.

So, the equation is as follows:

where p₁,p₂,...,p_N are the pages under consideration, M(p_i) is the set of pages that link to p_i, L(p_j) is the number of outbound links on page p_j, and N is the total number of pages.

The PageRank values are the entries of the dominant eigenvector In mathematics, eigenvalue, eigenvector, and eigenspace are related concepts in the field of linear algebra. The prefix eigen- is the German word for innate, idiosyncratic, own. Linear algebra studies linear transformations, which are represented by matrices acting on vectors. Eigenvalues, eigenvectors and eigenspaces are properties of a matrix of the modified adjacency matrix. This makes PageRank a particularly elegant metric: the eigenvector is

where R is the solution of the equation

where the adjacency function is 0 if page p_j does not link to p_i, and normalized such that, for each j

,

i.e. the elements of each column sum up to 1 (for more details see the computation section below). This is a variant of the eigenvector centrality Within graph theory and network analysis, there are various measures of the centrality of a vertex within a graph that determine the relative importance of a vertex within the graph measure used commonly in network analysis.

Because of the large eigengap of the modified adjacency matrix above, ^[8] the values of the PageRank eigenvector are fast to approximate (only a few iterations are needed).

As a result of Markov theory In probability theory and statistics, a Markov process, named after the Russian mathematician Andrey Markov, is a time-varying random phenomenon for which a specific property holds. In a common description, a stochastic process with the Markov property, or memorylessness, is one for which conditional on the present state of the system, its future, it can be shown that the PageRank of a page is the probability of being at that page after lots of clicks. This happens to equal t ^{− 1} where t is the expectation In probability theory and statistics, the expected value of a random variable is the integral of the random variable with respect to its probability measure of the number of clicks (or random jumps) required to get from the page back to itself.

The main disadvantage is that it favors older pages, because a new page, even a very good one, will not have many links unless it is part of an existing site (a site being a densely connected set of pages, such as Wikipedia Wikipedia is a free, web-based, collaborative, multilingual encyclopedia project supported by the non-profit Wikimedia Foundation. Its 16 million articles have been written collaboratively by volunteers around the world, and almost all of its articles can be edited by anyone with access to the site. Wikipedia was launched in 2001 by Jimmy Wales). The Google Directory (itself a derivative of the Open Directory Project The Open Directory Project , also known as Dmoz (from directory.mozilla.org, its original domain name), is a multilingual open content directory of World Wide Web links. It is owned by Netscape, but it is constructed and maintained by a community of volunteer editors) allows users to see results sorted by PageRank within categories. The Google Directory is the only service offered by Google where PageRank directly determines display order.^{[citation needed]} In Google's other search services (such as its primary Web search) PageRank is used to weight the relevance scores of pages shown in search results.

Several strategies have been proposed to accelerate the computation of PageRank.^[9]

Various strategies to manipulate PageRank have been employed in concerted efforts to improve search results rankings and monetize advertising links. These strategies have severely impacted the reliability of the PageRank concept, which seeks to determine which documents are actually highly valued by the Web community.

Google is known to penalize link farms On the World Wide Web, a link farm is any group of web sites that all hyperlink to every other site in the group. Although some link farms can be created by hand, most are created through automated programs and services. A link farm is a form of spamming the index of a search engine . Other link exchange systems are designed to allow individual and other schemes designed to artificially inflate PageRank. In December 2007 Google started actively penalizing sites selling paid text links. How Google identifies link farms and other PageRank manipulation tools are among Google's trade secrets A trade secret is a formula, practice, process, design, instrument, pattern, or compilation of information which is not generally known or reasonably ascertainable, by which a business can obtain an economic advantage over competitors or customers. In some jurisdictions, such secrets are referred to as "confidential information" or ".

Computation

To summarize, PageRank can be either computed iteratively or algebraically. The iterative method can be viewed differently as the power iteration method^[10][11], or power method. The basic mathematical operations performed in the iterative method and the power method are identical.

Iterative

In the former case, at t = 0, an initial probability distribution is assumed, usually

.

At each time step, the computation, as detailed above, yields

,

or in matrix notation

, (*)

where and is the column vector of length N containing only ones.

The matrix is defined as

i.e.,

,

where A denotes the adjacency matrix In mathematics and computer science, an adjacency matrix is a means of representing which vertices of a graph are adjacent to which other vertices. Another matrix representation for a graph is the incidence matrix of the graph and K is the diagonal matrix with the outdegrees in the diagonal.

The computation ends when for some small ε

,

i.e., when convergence is assumed.

Algebraic

In the latter case, for (i.e., in the steady state The concept of steady state has relevance in many fields, in particular thermodynamics and economics. Steady state is a more general situation than dynamic equilibrium. If a system is in steady state, then the recently observed behavior of the system will continue into the future. In stochastic systems, the probabilities that various different), the above equation (*) reads

. (**)

The solution is given by

,

with the identity matrix .

The solution exists and is unique for 0 < d < 1. This can be seen by noting that is by construction a stochastic matrix and hence has an eigenvalue equal to one because of the Perron-Frobenius theorem.

Power Method

If the matrix is a transition probability, i.e., column-stochastic with no columns consisting of just zeros and is a probability distribution (i.e., , where is matrix of all ones), Eq. (**) is equivalent to

. (***)

Hence PageRank is the principal eigenvector of . A fast and easy way to compute this is using the power method: starting with an arbitrary vector x, the operator is applied in succession, i.e.,

,

until

| x(t + 1) − x(t) | < ε.

Note that in Eq. (***) the matrix on the right-hand side in the parenthesis can be interpreted as

,

where is an initial probability distribution. In the current case

.

Finally, if has columns with only zero values, they should be replaced with the initial probability vector . In other words

,

where the matrix is defined as

,

with

In this case, the above two computations using only give the same PageRank if their results are normalized:

.

Efficiency

Depending on the framework used to perform the computation, the exact implementation of the methods, and the required accuracy of the result, the computation time of the these methods can vary greatly. Usually if the computation has to be performed many times (i.e., for growing networks) or the network size is large, the algebraic computation is slower and more memory hungry due to the inversion of the matrix.

Variations

Google Toolbar

The Google Toolbar Google Toolbar is an Internet browser toolbar available for Internet Explorer and Mozilla Firefox's PageRank feature displays a visited page's PageRank as a whole number between 0 and 10. The most popular websites have a PageRank of 10. The least have a PageRank of 0. Google has not disclosed the precise method for determining a Toolbar PageRank value. The displayed value is not the actual value Google uses so it is only a rough guide. ‘Toolbar’ PageRank is different than Google PageRank because the PageRank displayed in the toolbar is not 100% reflective of the way Google judges the value of a website.

The Google Toolbar's PageRank is updated approximately 4 times a year, so often shows out of date values. It was last updated on 3 April 2010.^[12]

SERP Rank

The SERP A search engine results page , is the listing of web pages returned by a search engine in response to a keyword query. The results normally include a list of web pages with titles, a link to the page, and a short description showing where the keywords have matched content within the page. A SERP may refer to a single page of links returned, or to (Search Engine Results Page) is the actual result returned by a search engine in response to a keyword query. The SERP consists of a list of links to web pages with associated text snippets. The SERP rank of a web page refers to the placement of the corresponding link on the SERP, where higher placement means higher SERP rank. The SERP rank of a web page is not only a function of its PageRank, but depends on a relatively large and continuously adjusted set of factors (over 200),^[13][14] commonly referred to by internet marketers as "Google Love"^[15]. SEO Search engine optimization is the process of improving the visibility of a web site or a web page in search engines via the "natural" or un-paid ("organic" or "algorithmic") search results. Other forms of search engine marketing (SEM) target paid listings. In general, the earlier (or higher on the page), and more (Search Engine Optimization) is aimed at achieving the highest possible SERP rank for a website or a set of web pages.

With the introduction of Google Places into the mainstream organic SERP, PageRank plays little to no role in ranking a business in the Local Business Results ^[16]. Albeit the theory of citations is still computed in their algorithm, PageRank is not a factor since Google ranks business listings and not web pages.

Google directory PageRank

The Google Directory This list of Google products includes all major desktop, mobile and online products released or acquired by Google Inc. They are either a gold release, in beta development, or part of the Google Labs initiative. This list also includes previous products, that have either been merged, discarded or renamed. Features of products, such as Web Search PageRank is an 8-unit measurement. These values can be viewed in the Google Directory. Unlike the Google Toolbar which shows the PageRank value by a mouseover of the green bar, the Google Directory does not show the PageRank as a numeric value but only as a green bar.

False or spoofed PageRank

While the PageRank shown in the Toolbar is considered to be derived from an accurate PageRank value (at some time prior to the time of publication by Google) for most sites, it must be noted that this value was at one time easily manipulated. A previous flaw was that any low PageRank page that was redirected, via a HTTP 302 response or a "Refresh" meta tag, to a high PageRank page caused the lower PageRank page to acquire the PageRank of the destination page. In theory a new, PR 0 page with no incoming links could have been redirected to the Google home page - which is a PR 10 - and then the PR of the new page would be upgraded to a PR10. This spoofing technique, also known as 302 Google Jacking, was a known failing or bug in the system. Any page's PageRank could have been spoofed to a higher or lower number of the webmaster's choice and only Google has access to the real PageRank of the page. Spoofing is generally detected by running a Google search for a URL with questionable PageRank, as the results will display the URL of an entirely different site (the one redirected to) in its results.

Manipulating PageRank

For search-engine optimization purposes, some companies offer to sell high PageRank links to webmasters.^[17] As links from higher-PR pages are believed to be more valuable, they tend to be more expensive. It can be an effective and viable marketing strategy to buy link advertisements on content pages of quality and relevant sites to drive traffic and increase a webmaster's link popularity. However, Google has publicly warned webmasters that if they are or were discovered to be selling links for the purpose of conferring PageRank and reputation, their links will be devalued (ignored in the calculation of other pages' PageRanks). The practice of buying and selling links is intensely debated across the Webmaster community. Google advises webmasters to use the nofollow HTML attribute value on sponsored links. According to Matt Cutts, Google is concerned about webmasters who try to game the system, and thereby reduce the quality and relevancy of Google search results.^[17]

The intentional surfer model

The original PageRank algorithm reflects the so-called random surfer model, meaning that the PageRank of a particular page is derived from the theoretical probability of visiting that page when clicking on links at random. However, real users do not randomly surf the web, but follow links according to their interest and intention. A page ranking model that reflects the importance of a particular page as a function of how many actual visits it receives by real users is called the intentional surfer model^[18]. The Google toolbar sends information to Google for every page visited, and thereby provides a basis for computing PageRank based on the intentional surfer model. The introduction of the nofollow attribute by Google to combat Spamdexing has the side effect that webmasters commonly use it on outgoing link to increase their own PageRank. This causes a loss of actual links for the Web crawlers to follow, thereby making the original PageRank algorithm based on the random surfer model potentially unreliable. Using information about users' browsing habits provided by the Google toolbar partly compensates for the loss of information caused by the nofollow attribute. The SERP rank of a page, which determines a page's actual placement in the search results, is based on a combination of the random surfer model (PageRank) and the intentional surfer model (browsing habits) in addition to other factors ^[19].

Other uses

A version of PageRank has recently been proposed as a replacement for the traditional Institute for Scientific Information (ISI) impact factor,^[20] and implemented at eigenfactor.org. Instead of merely counting total citation to a journal, the "importance" of each citation is determined in a PageRank fashion.

A similar new use of PageRank is to rank academic doctoral programs based on their records of placing their graduates in faculty positions. In PageRank terms, academic departments link to each other by hiring their faculty from each other (and from themselves). ^[21]

PageRank has been used to rank spaces or streets to predict how many people (pedestrians or vehicles) come to the individual spaces or streets.^[22][23]. In lexical semantics it has been used to perform Word Sense Disambiguation^[24] and to automatically rank WordNet synsets according to how strongly they possess a given semantic property, such as positivity or negativity. ^[25]

A dynamic weighting method similar to PageRank has been used to generate customized reading lists based on the link structure of Wikipedia. ^[26]

A Web crawler may use PageRank as one of a number of importance metrics it uses to determine which URL to visit during a crawl of the web. One of the early working papers ^[27] which were used in the creation of Google is Efficient crawling through URL ordering ^[28] , which discusses the use of a number of different importance metrics to determine how deeply, and how much of a site Google will crawl. PageRank is presented as one of a number of these importance metrics, though there are others listed such as the number of inbound and outbound links for a URL, and the distance from the root directory on a site to the URL.

The PageRank may also be used as a methodology to measure the apparent impact of a community like the Blogosphere on the overall Web itself. This approach uses therefore the PageRank to measure the distribution of attention in reflection of the Scale-free network paradigm.

In any ecosystem, a modified version of PageRank may be used to determine species that are essential to the continuing health of the environment.^[29]

Google's rel="nofollow" option

In early 2005, Google implemented a new value, "nofollow"^[30], for the rel attribute of HTML link and anchor elements, so that website developers and bloggers can make links that Google will not consider for the purposes of PageRank — they are links that no longer constitute a "vote" in the PageRank system. The nofollow relationship was added in an attempt to help combat spamdexing.

As an example, people could previously create many message-board posts with links to their website to artificially inflate their PageRank. With the nofollow value, message-board administrators can modify their code to automatically insert "" to all hyperlinks in posts, thus preventing PageRank from being affected by those particular posts. This method of avoidance, however, also has various drawbacks, such as reducing the link value of legitimate comments. (See: Spam in blogs#nofollow)

In an effort to manually control the flow of PageRank among pages within a website, many webmasters practice what is known as PageRank Sculpting^[31] - which is the act of strategically placing the nofollow attribute on certain internal links of a website in order to funnel PageRank towards those pages the webmaster deemed most important. This tactic has been used since the inception of the nofollow attribute, but the technique has been thought by many to have lost its effectiveness.^[32]

Removal from Google Webmaster Tools

On October 15, 2009, Google employee Susan Moskwa confirmed that the company had removed PageRank from its Webmaster Tools section. Her post said in part, "We’ve been telling people for a long time that they shouldn’t focus on PageRank so much; many site owners seem to think it's the most important metric for them to track, which is simply not true." ^[33]

See also

• EigenTrust — a decentralized PageRank algorithm
• Google bomb
• Google search
• Google matrix
• Hilltop algorithm
• Link love
• PigeonRank
• Power method — the iterative eigenvector algorithm used to calculate PageRank
• Search engine optimization
• SimRank - a measure of object-to-object similarity based on random-surfer model
• Topic-Sensitive PageRank
• TrustRank

Notes

1. ^ "Google Press Center: Fun Facts". www.google.com. http://www.google.com/press/funfacts.html. Retrieved 2009-10-05.
2. ^ Lisa M. Krieger (1 December 2005). "Stanford Earns $336 Million Off Google Stock". San Jose Mercury News, cited by redOrbit. http://www.redorbit.com/news/education/318480/stanford_earns_336_million_off_google_stock/. Retrieved 2009-02-25.
3. ^ Richard Brandt. "Starting Up. How Google got its groove". Stanford magazine. http://www.stanfordalumni.org/news/magazine/2004/novdec/features/startingup.html. Retrieved 2009-02-25.
4. ^ ^{a b} Google Technology
5. ^ ^{a b c d e} Sergey Brin, Larry Page (1998). "The Anatomy of a Large-Scale Hypertextual Web Search Engine". Proceedings of the 7th international conference on World Wide Web (WWW). Brisbane, Australia. pp. 107–117. http://dbpubs.stanford.edu:8090/pub/1998-8.
6. ^ David Vise and Mark Malseed (2005). The Google Story. pp. 37. ISBN ISBN 0-553-80457-X. http://www.thegooglestory.com/.
7. ^ Matt Cutts's blog: Straight from Google: What You Need to Know, see page 15 of his slides.
8. ^ Taher Haveliwala and Sepandar Kamvar. (March 2003). "The Second Eigenvalue of the Google Matrix" (PDF). Stanford University Technical Report. http://www-cs-students.stanford.edu/~taherh/papers/secondeigenvalue.pdf.
9. ^ Gianna M. Del Corso, Antonio Gullí, Francesco Romani (2005). "Fast PageRank Computation via a Sparse Linear System". Internet Mathematics 2 (3). http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.118.5422.
10. ^ Arasu, A. and Novak, J. and Tomkins, A. and Tomlin, J. (2002). "PageRank computation and the structure of the web: Experiments and algorithms". Proceedings of the Eleventh International World Wide Web Conference, Poster Track. Brisbane, Australia. pp. 107–117. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.18.5264&rep=rep1&type=pdf.
11. ^ http://arxiv.org/abs/1002.2858
12. ^ http://www.searchenginejournal.com/2010-google-toolbar-pagerank-update-pagerank-bunny/19708/Baker, Loren (April 5, 2010). 2010 Google Toolbar PageRank Update : PageRank Bunny. Search Engine Journal
13. ^ Aubuchon, Vaughn. "Google Ranking Factors - SEO Checklist". http://www.vaughns-1-pagers.com/internet/google-ranking-factors.htm.
14. ^ Fishkin, Rand; Jeff Pollard (April 2, 2007). "Search Engine Ranking Factors - Version 2". seomoz.org. http://www.seomoz.org/article/search-ranking-factors. Retrieved May 11, 2009.
15. ^ http://article-blog.thephantomwriters.com/google-love/2008/08/09/
16. ^ http://google.com/support/places/bin/answer.py?hl=en&answer=7091
17. ^ ^{a b} "How to report paid links". mattcutts.com/blog. April 14, 2007. http://www.mattcutts.com/blog/how-to-report-paid-links/. Retrieved 2007-05-28.
18. ^ Jøsang, A. (2007). "Trust and Reputation Systems". in Aldini, A. (PDF). Foundations of Security Analysis and Design IV, FOSAD 2006/2007 Tutorial Lectures.. 4677. Springer LNCS 4677. pp. 209–245. doi:10.1007/978-3-540-74810-6. http://www.unik.no/people/josang/papers/Jos2007-FOSAD.pdf.
19. ^ SEOnotepad. "Myth of the Google Toolbar Ranking". http://www.seonotepad.com/search-engines/google-seo/myth-of-the-google-toolbar-ranking/.
20. ^ Johan Bollen, Marko A. Rodriguez, and Herbert Van de Sompel. (December 2006). "Journal Status". Scientometrics 69 (3). http://www.arxiv.org/abs/cs.GL/0601030.
21. ^ Benjamin M. Schmidt and Matthew M. Chingos (2007). "Ranking Doctoral Programs by Placement: A New Method" (PDF). PS: Political Science and Politics 40 (July): 523–529. http://www.people.fas.harvard.edu/~chingos/rankings_paper.pdf.
22. ^ B. Jiang (2006). "Ranking spaces for predicting human movement in an urban environment" (PDF). International Journal of Geographical Information Science 23: 823–837. doi:10.1080/13658810802022822. http://arxiv.org/abs/physics/0612011.
23. ^ Jiang B., Zhao S., and Yin J. (2008). "Self-organized natural roads for predicting traffic flow: a sensitivity study" (PDF). Journal of Statistical Mechanics: Theory and Experiment P07008. http://arxiv.org/abs/0804.1630.
24. ^ Roberto Navigli, Mirella Lapata. "An Experimental Study of Graph Connectivity for Unsupervised Word Sense Disambiguation". IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 32(4), IEEE Press, 2010, pp. 678-692.
25. ^ Andrea Esuli and Fabrizio Sebastiani. "PageRanking WordNet synsets: An Application to Opinion-Related Properties" (PDF). In Proceedings of the 35th Meeting of the Association for Computational Linguistics, Prague, CZ, 2007, pp. 424-431. http://nmis.isti.cnr.it/sebastiani/Publications/ACL07.pdf. Retrieved June 30, 2007.
26. ^ Wissner-Gross, A. D. (2006). "Preparation of topical readings lists from the link structure of Wikipedia". Proceedings of the IEEE International Conference on Advanced Learning Technology (Rolduc, Netherlands): 825. doi:10.1109/ICALT.2006.1652568.
27. ^ "Working Papers Concerning the Creation of Google". Google. http://dbpubs.stanford.edu:8091/diglib/pub/projectdir/google.html. Retrieved November 29, 2006.
28. ^ Cho, J., Garcia-Molina, H., and Page, L. (1998). "Efficient crawling through URL ordering". Proceedings of the seventh conference on World Wide Web (Brisbane, Australia).
29. ^ Google trick tracks extinctions
30. ^ "Preventing Comment Spam". Google. http://googleblog.blogspot.com/2005/01/preventing-comment-spam.html. Retrieved January 1, 2005.
31. ^ http://www.seomoz.org/blog/pagerank-sculpting-parsing-the-value-and-potential-benefits-of-sculpting-pr-with-nofollow
32. ^ http://www.mattcutts.com/blog/pagerank-sculpting/
33. ^ Susan Moskwa, "PageRank Distribution Removed From WMT", http://www.google.com/support/forum/p/Webmasters/thread?tid=6a1d6250e26e9e48&hl=en, retrieved October 16, 2009 }

References

• Altman, Alon; Moshe Tennenholtz (2005). "Ranking Systems: The PageRank Axioms" (PDF). Proceedings of the 6th ACM conference on Electronic commerce (EC-05). Vancouver, BC. http://stanford.edu/~epsalon/pagerank.pdf. Retrieved 2008-02-05.
• Cheng, Alice; Eric J. Friedman (2006-06-11). "Manipulability of PageRank under Sybil Strategies" (PDF). Proceedings of the First Workshop on the Economics of Networked Systems (NetEcon06). Ann Arbor, Michigan. http://www.cs.duke.edu/nicl/netecon06/papers/ne06-sybil.pdf. Retrieved 2008-01-22.
• Farahat, Ayman; LoFaro, Thomas; Miller, Joel C.; Rae, Gregory and Ward, Lesley A. (2006). "Authority Rankings from HITS, PageRank, and SALSA: Existence, Uniqueness, and Effect of Initialization". SIAM Journal on Scientific Computing 27 (4): 1181–1201. doi:10.1137/S1064827502412875.
• Haveliwala, Taher; Jeh, Glen and Kamvar, Sepandar (2003). "An Analytical Comparison of Approaches to Personalizing PageRank" (PDF). Stanford University Technical Report. http://www-cs-students.stanford.edu/~taherh/papers/comparison.pdf.
• Langville, Amy N.; Meyer, Carl D. (2003). "Survey: Deeper Inside PageRank". Internet Mathematics 1 (3).
• Langville, Amy N.; Meyer, Carl D. (2006). Google's PageRank and Beyond: The Science of Search Engine Rankings. Princeton University Press. ISBN 0-691-12202-4.
• Page, Lawrence; Brin, Sergey; Motwani, Rajeev and Winograd, Terry (1999). The PageRank citation ranking: Bringing order to the Web. http://dbpubs.stanford.edu:8090/pub/showDoc.Fulltext?lang=en&doc=1999-66&format=pdf&compression=.
• Richardson, Matthew; Domingos, Pedro (2002). "The intelligent surfer: Probabilistic combination of link and content information in PageRank" (PDF). Proceedings of Advances in Neural Information Processing Systems. 14. http://www.cs.washington.edu/homes/pedrod/papers/nips01b.pdf.

External links

• Our Search: Google Technology by Google
• How Google Finds Your Needle in the Web's Haystack by the American Mathematical Society
• Original PageRank U.S. Patent- Method for node ranking in a linked database - September 4, 2001
• PageRank U.S. Patent - Method for scoring documents in a linked database - September 28, 2004
• PageRank U.S. Patent - Method for node ranking in a linked database - June 6, 2006
• PageRank U.S. Patent - Scoring documents in a linked database - September 11, 2007
• Scientist discovers PageRank-type algorithm from the 1940s - February 17, 2010

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