*The Business Professor*, updated March 31, 2019, last accessed August 13, 2020, https://thebusinessprofessor.com/lesson/page-rank-definition/.

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**PageRank Definition**

An algorithm that Google search uses for ranking websites in its search engine results is called PageRank. This term is on the name of Larry Page, who is one of the pioneers of Google. PageRank is a method of measuring how much important web pages are. Google says:

PageRank counts the quality and no. of page links to roughly estimate the importance of a website. It is assumed that the more important a website is, the more links it will get from other sites.

Nowadays, Google does not use the PageRank algorithm only for ordering search results. But the company used it the 1st time and everyone knows about it.

**A Little More on What is Page Rank**

PageRank is used for link analysis. It has access to all set of documents containing hyperlinks, for example, WWW (World Wide Web). To every element of this set, it allocates a numeric weighting. The main purpose is to measure the comparative importance in the set. We can apply it to a group of entities with references and reciprocal quotations. Let the element is represented as E and the numeric weight as PageRank of E. We can denote it as {\displaystyle PR(E).} Author Rank is another factor which can show an entity’s importance.

A PageRank displays results using a mathematical algorithm that is based on the web graph. All pages of the World Wide Web create hyperlinks as edges and web graph as nodes considering authority hubs, e.g. usa.gov or cnn.com. The value of rank shows the importance of a specific page. A page hyperlink is counted as a vote of support. Google defines PageRank recursively. It is based on the PageRank metrics and the number of all web pages linking to it. We call them the incoming links. A web page which has high PageRank and linked to a number of pages, itself, gets a high rank.

Page and Brin published their paper and after that many academic papers have been published on PageRank. Practically, its concept has critics of manipulation. To identify the falsely affected rankings of PageRank, research has been carried out. The objective is to find an efficient way of ignoring links from falsely affected PageRank documents.

Advantages of running a website with high PageRank:

- If the PageRank of a home page (main page) is higher, Google will more likely spider your website frequently.
- Higher PageRank = Deeper crawlings and less supplemental problems
- Webmasters will send you more offers of link exchange.
- The cycle of Google’s crawling gets better. This is because of the amount of incoming and inbound links, you have.
- The spacing value of your ads will enhance so that you can sell more advertisements.
- Your website will get more traffic due to the enhanced number of incoming links.
- Credentials. High PageRank is considered to show that you have expertise in the niche of your blog.
- More visitors will comment on your website because of establishing credentials.

**References for Page Rank**

- https://pr.efactory.de/e-pagerank-algorithm.shtml
- https://www.practicalecommerce.com/pagerank-what-is-it-and-how-do-you-calculate-it
- https://en.wikipedia.org/wiki/PageRank

**Academic Research on PageRank**

The **PageRank **citation ranking: Bringing order to the web., **Page, L., Brin, S., Motwani, R., & Winograd, T. (1999). Stanford InfoLab.** There are many factors counted for the importance of a website, e.g, interesting information and readers’ involvement, but this is subjective importance. The main factor of its objective importance is PageRank. It is a way of rating website pages mechanically. The authors describe how to count it effectively for numerous pages and apply it for searching and navigating.

• Topic-sensitive **pagerank**, **Haveliwala, T. H. (2002, May). In ***Proceedings of the 11th international conference on World Wide Web*** (pp. 517-526). ACM.** To get more exact search engine results, the authors present PageRank vectors. They show that it is possible to get more exact rankings. For general keyword search results, they estimate topic-sensitive PR scores for web pages answering the query with the help of query keywords topic.

• Deeper inside **pagerank**, **Langville, A. N., & Meyer, C. D. (2004). ***Internet Mathematics***, ***1***(3), 335-380.** This paper presents a complete survey of all problems related to PageRank. The authors explain the basic PR model, storage problems, appropriate solutions, and possible amendments to the basic approach. They draw new results and work on a detailed reference list. They speculate about interesting areas of research in future.

• Inside **pagerank**, **Bianchini, M., Gori, M., & Scarselli, F. (2005). ***ACM Transactions on Internet Technology (TOIT)***, ***5***(1), 92-128.** PageRank is a technique to score website pages based on the web connectivity. The authors reveal its basic attributes and parameters to be used in the computation. They critically analyse page score distribution, dangling pages (pages which have no outlinks) and the secret to promoting web pages.

• Weighted **pagerank **algorithm, **Xing, W., & Ghorbani, A. (2004, May). In ***Communication Networks and Services Research, 2004. Proceedings. Second Annual Conference on***(pp. 305-314). IEEE.** The main purpose of a website is to make relevant information accessible to the users. So, it is utmost important to find their needs, interests and behaviour. This paper uses 2 algorithms of page ranking, i.e. PageRank and HITS. The performance of these algorithms has been improved by using many algorithms along with these ones. Weighted Page Rank is an extended form of the PR algorithm. It makes the distribution of scores on pages popularity. Hence, its performance is better than the conventional PR algorithm.

• Efficient computation of **PageRank**, **Haveliwala, T. (1999). Stanford.** This research introduces a ranking measure for hypertext docs. PR for fairly large web subgraphs has been computed on the machine. The authors present many techniques to analyze the PR convergence on the basis of induced ordering of the web pages. Ultimately, the outcome is helpful to determine the no. of iterations required to get a useful PR assignment in absence as well as the presence of search queries.

• Local graph partitioning using **pagerank **vectors, **Andersen, R., Chung, F., & Lang, K. (2006, October). In ***null*** (pp. 475-486). IEEE.** The writers propose a local partitioning algorithm as an invariant of PR with a particular initial distribution. The result is that vertices ordering generated by a PR vector shows a cut with little conductance, i.e. (O(radic(Phi log k)) where Phi is the conductance and k is the volume. The authors merge the small sets and get a cut with oslash conductance and nearly optimal balance in O(m log4 m/oslash) time where m shows the no. of edges.

• Extrapolation methods for accelerating **PageRank **computations, **Kamvar, S. D., Haveliwala, T. H., Manning, C. D., & Golub, G. H. (2003, May). In ***Proceedings of the 12th international conference on World Wide Web*** (pp. 261-270). ACM.** The authors propose a new algorithm to speed up PR computation. It is named as Quadratic Extrapolation (QE). It boosts the convergence of the original Power method. Using Quadratic Extrapolation, the PR computation accelerates from 25 to 300 percent on a web graph having eighty million nodes with the least overhead. So, their contribution to the PR community is very useful.

• Topic-sensitive **pagerank**: A context-sensitive ranking algorithm for web search, **Haveliwala, T. H. (2003). ***IEEE transactions on knowledge and data engineering***, ***15***(4), 784-796.** The PR algorithm calculates a single vector. The authors present a couple of PR vectors to produce more accurate results of a search query. For satisfying general search queries, the authors calculate the topic-sensitive PR score. On the same scheme, the generic PR vector has been used to rank pages more accurately.

• Adaptive methods for the computation of **PageRank**, **Kamvar, S., Haveliwala, T., & Golub, G. (2004). ***Linear Algebra and its Applications***, ***386***, 51-65. **The convergence patterns of web pages have a non-uniform distribution in the PR algorithm. The authors find that the slow converging web pages have usually high PR. Using this observation, the authors develop a simple algorithm for making the computation of PR faster (almost 30%). It is called Adaptive PageRank.

• Exploiting the block structure of the web for computing **pagerank**, **Kamvar, S., Haveliwala, T., Manning, C., & Golub, G. (2003). Stanford.** Most of the hyperlinks connect to web pages on a host with other web pages of the same host. In order to make the PR computation faster, the authors use 3 stage algorithm (i) Local PR for every host (ii) weighting of local PRs according to the importance of the underlying host (iii) standard PR algorithm to calculate the weighted aggregate of local PRs. The authors present a variant of this 3 stage algorithm.