Google's PageRank Explained

PageRank is a numeric value that represents how important a page is on the web. Google figures that when one page links to another page, it is effectively casting a vote for the other page. The more votes that are cast for a page, the more important the page must be. Also, the importance of the page that is casting the vote determines how important the vote itself is. Google calculates a page's importance from the votes cast for it. How important each vote is is taken into account when a page's PageRank is calculated.

PageRank is Google's way of deciding a page's importance. It matters because it is one of the factors that determines a page's ranking in the search results. It isn't the only factor that Google uses to rank pages, but it is an important one.

From here on in, we'll occasionally refer to PageRank as "PR".

Notes:
Not all links are counted by Google. For instance, they filter out links from known link farms. Some links can cause a site to be penalized by Google. They rightly figure that webmasters cannot control which sites link to their sites, but they can control which sites they link out to. For this reason, links into a site cannot harm the site, but links from a site can be harmful if they link to penalized sites. So be careful which sites you link to. If a site has PR0, it is usually a penalty, and it would be unwise to link to it.

To calculate the PageRank for a page, all of its inbound links are taken into account. These are links from within the site and links from outside the site.

PR(A) = (1-d) + d(PR(t1)/C(t1) + ... + PR(tn)/C(tn))

That's the equation that calculates a page's PageRank. It's the original one that was published when PageRank was being developed, and it is probable that Google uses a variation of it but they aren't telling us what it is. It doesn't matter though, as this equation is good enough.

In the equation 't1 - tn' are pages linking to page A, 'C' is the number of outbound links that a page has and 'd' is a damping factor, usually set to 0.85.

We can think of it in a simpler way:-

a page's PageRank = 0.15 + 0.85 * (a "share" of the PageRank of every page that links to it)

"share" = the linking page's PageRank divided by the number of outbound links on the page.

A page "votes" an amount of PageRank onto each page that it links to. The amount of PageRank that it has to vote with is a little less than its own PageRank value (its own value * 0.85). This value is shared equally between all the pages that it links to.

From this, we could conclude that a link from a page with PR4 and 5 outbound links is worth more than a link from a page with PR8 and 100 outbound links. The PageRank of a page that links to yours is important but the number of links on that page is also important. The more links there are on a page, the less PageRank value your page will receive from it.

If the PageRank value differences between PR1, PR2,.....PR10 were equal then that conclusion would hold up, but many people believe that the values between PR1 and PR10 (the maximum) are set on a logarithmic scale, and there is very good reason for believing it. Nobody outside Google knows for sure one way or the other, but the chances are high that the scale is logarithmic, or similar. If so, it means that it takes a lot more additional PageRank for a page to move up to the next PageRank level that it did to move up from the previous PageRank level. The result is that it reverses the previous conclusion, so that a link from a PR8 page that has lots of outbound links is worth more than a link from a PR4 page that has only a few outbound links.

Whichever scale Google uses, we can be sure of one thing. A link from another site increases our site's PageRank. Just remember to avoid links from link farms.

Note that when a page votes its PageRank value to other pages, its own PageRank is not reduced by the value that it is voting. The page doing the voting doesn't give away its PageRank and end up with nothing. It isn't a transfer of PageRank. It is simply a vote according to the page's PageRank value. It's like a shareholders meeting where each shareholder votes according to the number of shares held, but the shares themselves aren't given away. Even so, pages do lose some PageRank indirectly, as we'll see later.

Ok so far? Good. Now we'll look at how the calculations are actually done.

For a page's calculation, its existing PageRank (if it has any) is abandoned completely and a fresh calculation is done where the page relies solely on the PageRank "voted" for it by its current inbound links, which may have changed since the last time the page's PageRank was calculated.

The equation shows clearly how a page's PageRank is arrived at. But what isn't immediately obvious is that it can't work if the calculation is done just once. Suppose we have 2 pages, A and B, which link to each other, and neither have any other links of any kind. This is what happens:-

Step 1: Calculate page A's PageRank from the value of its inbound links

Page A now has a new PageRank value. The calculation used the value of the inbound link from page B. But page B has an inbound link (from page A) and its new PageRank value hasn't been worked out yet, so page A's new PageRank value is based on inaccurate data and can't be accurate.

Step 2: Calculate page B's PageRank from the value of its inbound links

Page B now has a new PageRank value, but it can't be accurate because the calculation used the new PageRank value of the inbound link from page A, which is inaccurate.

It's a Catch 22 situation. We can't work out A's PageRank until we know B's PageRank, and we can't work out B's PageRank until we know A's PageRank.

Now that both pages have newly calculated PageRank values, can't we just run the calculations again to arrive at accurate values? No. We can run the calculations again using the new values and the results will be more accurate, but we will always be using inaccurate values for the calculations, so the results will always be inaccurate.

The problem is overcome by repeating the calculations many times. Each time produces slightly more accurate values. In fact, total accuracy can never be achieved because the calculations are always based on inaccurate values. 40 to 50 iterations are sufficient to reach a point where any further iterations wouldn't produce enough of a change to the values to matter. This is precisiely what Google does at each update, and it's the reason why the updates take so long.

One thing to bear in mind is that the results we get from the calculations are proportions. The figures must then be set against a scale (known only to Google) to arrive at each page's actual PageRank. Even so, we can use the calculations to channel the PageRank within a site around its pages so that certain pages receive a higher proportion of it than others.

NOTE:
You may come across explanations of PageRank where the same equation is stated but the result of each iteration of the calculation is added to the page's existing PageRank. The new value (result + existing PageRank) is then used when sharing PageRank with other pages. These explanations are wrong for the following reasons:-

1. They quote the same, published equation - but then change it

from PR(A) = (1-d) + d(......) to PR(A) = PR(A) + (1-d) + d(......)

It isn't correct, and it isn't necessary.

2. We will be looking at how to organize links so that certain pages end up with a larger proportion of the PageRank than others. Adding to the page's existing PageRank through the iterations produces different proportions than when the equation is used as published. Since the addition is not a part of the published equation, the results are wrong and the proportioning isn't accurate.

According to the published equation, the page being calculated starts from scratch at each iteration. It relies solely on its inbound links. The 'add to the existing PageRank' idea doesn't do that, so its results are necessarily wrong.

Fact: A website has a maximum amount of PageRank that is distributed between its pages by internal links.

The maximum PageRank in a site equals the number of pages in the site * 1. The maximum is increased by inbound links from other sites and decreased by outbound links to other sites. We are talking about the overall PageRank in the site and not the PageRank of any individual page. You don't have to take my word for it. You can reach the same conclusion by using a pencil and paper and the equation.

Fact: The maximum amount of PageRank in a site increases as the number of pages in the site increases.

The more pages that a site has, the more PageRank it has. Again, by using a pencil and paper and the equation, you can come to the same conclusion. Bear in mind that the only pages that count are the ones that Google knows about.

Fact: By linking poorly, it is possible to fail to reach the site's maximum PageRank, but it is not possible to exceed it.

Poor internal linkages can cause a site to fall short of its maximum but no kind of internal link structure can cause a site to exceed it. The only way to increase the maximum is to add more inbound links and/or increase the number of pages in the site.

Cautions: Whilst I thoroughly recommend creating and adding new pages to increase a site's total PageRank so that it can be channeled to specific pages, there are certain types of pages that should not be added. These are pages that are all identical or very nearly identical and are known as cookie-cutters. Google considers them to be spam and they can trigger an alarm that causes the pages, and possibly the entire site, to be penalized. Pages full of good content are a must.

What can we do with this 'overall' PageRank?

We are going to look at some example calculations to see how a site's PageRank can be manipulated, but before doing that, I need to point out that a page will be included in the Google index only if one or more pages on the web link to it. That's according to Google. If a page is not in the Google index, any links from it can't be included in the calculations.

A dangling link is a link to a page that has no links going from it, or a link to a page that Google hasn't indexed. In both cases Google removes the links shortly after the start of the calculations and reinstates them shortly before the calculations are finished. In this way, their effect on the PageRank of other pages in minimal.

The results shown in Example 1 (right diag.) are wrong because page B has no links going from it, and so the link from page A to page B is dangling and would be removed from the calculations. The results of the calculations would show all three pages as having 0.15.

It may suit site functionality to link to pages that have no links going from them without losing any PageRank from the other pages but it would be waste of potential PageRank.

Although it may be functionally good to link to pages within the site without those pages linking out again, it is bad for PageRank. It is pointless wasting PageRank unnecessarily, so always make sure that every page in the site links out to at least one other page in the site.

Inbound links (links into the site from the outside) are one way to increase a site's total PageRank. The other is to add more pages. Where the links come from doesn't matter. Google recognizes that a webmaster has no control over other sites linking into a site, and so sites are not penalized because of where the links come from. There is an exception to this rule but it is rare and doesn't concern this article. It isn't something that a webmaster can accidentally do.

Outbound links are a drain on a site's total PageRank. They leak PageRank. To counter the drain, try to ensure that the links are reciprocated. Because of the PageRank of the pages at each end of an external link, and the number of links out from those pages, reciprocal links can gain or lose PageRank. You need to take care when choosing where to exchange links.

When PageRank leaks from a site via a link to another site, all the pages in the internal link structure are affected. (This doesn't always show after just 1 iteration). The page that you link out from makes a difference to which pages suffer the most loss. Without a program to perform the calculations on specific link structures, it is difficult to decide on the right page to link out from, but the generalization is to link from the one with the lowest PageRank.

Many websites need to contain some outbound links that are nothing to do with PageRank. Unfortunately, all 'normal' outbound links leak PageRank. But there are 'abnormal' ways of linking to other sites that don't result in leaks. PageRank is leaked when Google recognizes a link to another site. The answer is to use links that Google doesn't recognize or count. These include form actions and links contained in javascript code.

Form actions
A form's 'action' attribute does not need to be the url of a form parsing script. It can point to any html page on any site. Try it.

Example:
<form name="myform" action="http://www.domain.com/somepage.html">
<a href="javascript:document.myform.submit()">Click here</a>

To be really sneaky, the action attribute could be in some javascript code rather than in the form tag, and the javascript code could be loaded from a 'js' file stored in a directory that is barred to Google's spider by the robots.txt file.

Javascript
Example: <a href="javascript:goto('wherever')">Click here</a>

Like the form action, it is sneaky to load the javascript code, which contains the urls, from a seperate 'js' file, and sneakier still if the file is stored in a directory that is barred to googlebot by the robots.txt file.

The "rel" attribute
As of 18th January 2005, Google, together with other search engines, is recognising a new attribute to the anchor tag. The attribute is "rel", and it is used as follows:-
<a href="http://www.domain.com/somepage.html" rel="nofollow">link text</a>
The attribute tells Google to ignore the link completely. The link won't help the target page's PageRank, and it won't help its rankings. It is as though the link doesn't exist. With this attribute, there is no longer any need for javascript, forms, or any other method of hiding links from Google.

The Google toolbar range is from 1 to 10. (They sometimes show 0, but that figure isn't believed to be a PageRank calculation result). What Google does is divide the full range of actual PageRanks on the web into 10 parts - each part is represented by a value as shown in the toolbar. So the toolbar values only show what part of the overall range a page's PageRank is in, and not the actual PageRank itself. The numbers in the toolbar are just labels.

Whether or not the overall range is divided into 10 equal parts is a matter for debate - Google aren't saying. But because it is much harder to move up a toolbar point at the higher end than it is at the lower end, many people (including me) believe that the divisions are based on a logarithmic scale, or something very similar, rather than the equal divisions of a linear scale.

Let's assume that it is a logarithmic, base 10 scale, and that it takes 10 properly linked new pages to move a site's important page up 1 toolbar point. It will take 100 new pages to move it up another point, 1000 new pages to move it up one more, 10,000 to the next, and so on. That's why moving up at the lower end is much easier that at the higher end.

In reality, the base is unlikely to be 10. Some people think it is around the 5 or 6 mark, and maybe even less. Even so, it still gets progressively harder to move up a toolbar point at the higher end of the scale.

Note that as the number of pages on the web increases, so does the total PageRank on the web, and as the total PageRank increases, the positions of the divisions in the overall scale must change. As a result, some pages drop a toolbar point for no 'apparent' reason. If the page's actual PageRank was only just above a division in the scale, the addition of new pages to the web would cause the division to move up slightly and the page would end up just below the division. Google's index is always increasing and they re-evaluate each of the pages on more or less a monthly basis. It's known as the "Google dance". When the dance is over, some pages will have dropped a toolbar point. A number of new pages might be all that is needed to get the point back after the next dance.

The toolbar value is a good indicator of a page's PageRank but it only indicates that a page is in a certain range of the overall scale. One PR5 page could be just above the PR5 division and another PR5 page could be just below the PR6 division - almost a whole division (toolbar point) between them.

To a spider, www.domain.com/, domain.com/, www.domain.com/index.html and domain.com/index.html are different urls and, therefore, different pages. Surfers arrive at the site's home page whichever of the urls are used, but spiders see them as individual urls, and it makes a difference when working out the PageRank. It is better to standardize the url you use for the site's home page. Otherwise each url can end up with a different PageRank, whereas all of it should have gone to just one url.

If you think about it, how can a spider know the filename of the page that it gets back when requesting www.domain.com/ ? It can't. The filename could be index.html, index.htm, index.php, default.html, etc. The spider doesn't know. If you link to index.html within the site, the spider could compare the 2 pages but that seems unlikely. So they are 2 urls and each receives PageRank from inbound links. Standardizing the home page's url ensures that the Pagerank it is due isn't shared with ghost urls.

The Google toolbar
If you have the Google toolbar installed in your browser, you will be used to seeing each page's PageRank as you browse the web. But all isn't always as it seems. Many pages that Google displays the PageRank for haven't been indexed in Google and certainly don't have any PageRank in their own right. What is happening is that one or more pages on the site have been indexed and a PageRank has been calculated. The PageRank figure for the site's pages that haven't been indexed is allocated on the fly - just for your toolbar. The PageRank itself doesn't exist.

It's important to know this so that you can avoid exchanging links with pages that really don't have any PageRank of their own. Before making exchanges, search for the page on Google to make sure that it is indexed.

Sub-directories
Some people believe that Google drops a page's PageRank by a value of 1 for each sub-directory level below the root directory. E.g. if the value of pages in the root directory is generally around 4, then pages in the next directory level down will be generally around 3, and so on down the levels. Other people (including me) don't accept that at all. Either way, because some spiders tend to avoid deep sub-directories, it is generally considered to be beneficial to keep directory structures shallow (directories one or two levels below the root).

ODP and Yahoo!
It used to be thought that Google gave a Pagerank boost to sites that are listed in the Yahoo! and ODP (a.k.a. DMOZ) directories, but these days general opinion is that they don't. There is certainly a PageRank gain for sites that are listed in those directories, but the reason for it is now thought to be this:-

Google spiders the directories just like any other site and their pages have decent PageRank and so they are good inbound links to have. In the case of the ODP, Google's directory is a copy of the ODP directory. Each time that sites are added and dropped from the ODP, they are added and dropped from Google's directory when they next update it. The entry in Google's directory is yet another good, PageRank boosting, inbound link. Also, the ODP data is used for searches on a myriad of websites - more inbound links!

Listings in the ODP are free but, because sites are reviewed by hand, it can take quite a long time to get in. The sooner a working site is submitted, the better.