# What is PageRank?

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## Introduction

The notion “Google PageRank” is one of the most important moments in the work of Google search engine. In addition to other parameters that affect the positions of websites in the search results, knowledge of the model of PageRank is necessary for understanding the process of search and for optimizers when they are promoting their websites in the search engines.

In this article I would like to present the mathematical foundations of computation of PageRank used in any domain. For the beginning, let’s take for the axiom that, counting PageRank, Google doesn’t take into consideration “Racial” affiliation links, their “language group” or the “appearance”. All pages in Internet are equal to each other and their weight will determined only by authority of pages donor referring to them.

By other words, we came to the notion PageRank that reflects the authority of your page with the help of links (“hearings”) from other pages. It’s clear that the more links leading to your page, the more weight or authority you have.

## Definition of PageRank

PageRank (PR) is numerical value; it’s a measure of importance of a page in Search Engine Google. It depends on the number of external links leading to this page and on their weight and importance.  By other words, PR of any page depends on quantity and quality of external links leading to this page. And if we talk in mathematical language, PR is algorithm for calculating authority of pages used by search engine system Google. PR is not the main but one of the main factors in websites ranking.

It worth to notice that counting PageRank Google doesn’t take into account all existing links leading to the page. Counting it removes all websites created for paid link placing etc. Some links may not only not being in counting but make a bad reputation to the page.

## The classical model of representation of PageRank

The documentation about PR introdused by Sergey Brin and Larry Page you may find following the next link https://devaka.ru/files/The_PageRank_Citation_Ranking.pdf

The main formula describing PR is the following:

d – damping coefficient, it reflects what percentage of weight or authority can give a page donor to an acceptor page. Normally it is taken equal to 0.85, it means that page can give 85% of its authority (it’s distributed among all acceptors referenced by donor). In other sources d is the probability that the user will move to one of the acceptors and doesn’t close the window of browser.

n – the number of pages linking to a page-acceptor (those that are without any penalties)

Ti – i-th page linking to a page-acceptor

C – munber of external links on the page donor.

## Toolbar PageRank representation

As there can be many referencing pages and the total number of pages in the Google search engine is large and this number grows, it wouldn’t right for webmasters to represent the weight of the page in absolute values. For this, the notion “LPR — ToolBar PageRank” was introduced. It has value from 0 to 10 (Green scale in Google ToolBar)

For keep the authority of pages in limits from 0 to 10 webmasters use this logarithmic scale:

Where base – is the base of the logarithm depending on the number of pages in search engine. Some people take it equal to 7;

a – a reduction coefficient that obeys the inequality 0 < a ≤ 1. Optimizers take it equal to 1 for simplifying the calculations.

From the foregoing, it’s wrong to conclude that zero TLPR means that the PageRank is also zero. According the first formula we can see that having n=0, we receive PRmin= (1-d) = 0.15.

This value corresponds to TLPR ≈ -1. With these (negative) value of ToolBar PR, PR = N / A (or not yet determined), but these (negative) value also affects the distribution of weight between the link-acceptors. It worth to notice that ToolBar value is intended only for webmasters in Google ToolBar.

## Conclusion

Knowing now the principles of calculating Google PageRank, we can easily calculate on what pages we can place our links and how much links we need to obtain a needed PR. We can also forecast PR of pages. If we have a new website with more than 10 000, they are relinked properly and each page refers to the main page, the home page will get a good weight from these links. A bit of math on this.

PRmin = 0.15;

PR = 0.15 + 0.85 * 20000/10; (taking into account average 10 references on page)

TL*PR* = Log(1700.15, 7) = 3.823 ≈ 4

Here is a good example of a good PR without any links from other websites.

• How to increase my website PR?

There are many ways to increase the PR of your website pages but the main idea is quality links from other sites. You can use for this different catalogues, social media websites, forums, blogs etc. Nevertheless, never place the links referring to your website on all sites you see. There are not only PageRank influencing the search results but TrustRunk.

• Does it happen a negative PR?

No, doesn’t. Real PR minimum is equal to 0.15, minimum ToolBar is equal to 0.

• When PageRank is updated?

ToolBar PageRank is updated once per 2-4 months, for real PR updates are more often. You can see your current PR in the catalogue Google DMOZ, if your website was added in this catalogue.

• Does the language of link influence on PR?

No, doesn’t. Only quantity and quality of referring links influence on PR.

• Does the number of visitors influence on Google PageRank?

No, also no.

• Does the PR from images can give PR to the page?

PR from images can give PR to the page but if the image is a link referring somewhere.

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