11. PR0 - Google's PageRank 0 Penalty (continued)

BadRank as the
Opposite of PageRank

The theoretical approach for
PR0 as it is presented here was
initially brought up by Raph Levien (www.advogato.org/person/raph). We want to introduce a technique that -
just like PageRank - analyzes link structures, but, that unlike PageRank

does not determine the general importance of a web page but rather measures its negative characteristics. For the sake of simplicity this technique shall be called "BadRank".

	BadRank is in priciple based on "linking to bad neighbourhoods". If one page links to another page with a high BadRank, the first page gets a high BadRank itself through this link. The similarities to PageRank are

BR(A) = E(A) (1-d) + d (BR(T1)/C(T1) + ... + BR(Tn)/C(Tn))

where

BR(A) is the BadRank of page A,
BR(Ti) is the BadRank of pages Ti which are outbound links of page A,
C(Ti) is here the number of inbound links of page Ti and
d is the again necessary damping factor.

In the previously discussed modifications of the PageRank algorithm, E(A) represented the special evaluation of certain web pages. Regarding the BadRank algorithm, this value reflects if a page was detected by a spam filter or not. Without the value E(A), the BadRank algorithm would be useless because it was nothing but another analysis of link structures which would not take any further criteria into account.

By means of the BadRank algorithm, first of all, spam pages can be evaluated. A filter assigns a numeric value E(A) to them, which can, for example, be based on the degree of spamming or maybe even better on their PageRank. Thereby, again, the sum of all E(A) has to equal the total number of web pages. In the course of an iterative computation, BadRank is not only transfered to pages which link to spam pages. In fact, BadRank is able to identify regions of the web where spam tends to occur relatively often, just as PageRank identifies regions of the web which are of general importance.

	Of course, BadRank and PageRank have significant differences, especially, because of using outbound and inbound links, respectively. Our example shows a simple, hierarchically structured website that reflects common link structures pretty well. Each page links to every page which is on a higher hierachical level and on its branch of the website's tree structure. Each page links to pages which are arranged hierarchically directly below them and, additionally, pages on the same branch and the same

Level 0 1 2	inbound Links 6 4 2	outbound Links 2 4 3

As to be expected, regarding inbound links, a hierarchical gradation from the index page downwards takes place. In contrast, we find the highest number of outbound links on the website's mid-level. We can see similar results, when we add another level of pages to our website while the above described linking rules stay the same.

Level 0 1 2 3	inbound Links 1 8 4 2	outbound Links 2 4 5 4

Again, there is a concentration of outbound links on the website's mid-level. But most of all, the outbound links are much more evenly distributed than the inbound links.

If we assign a value of 100 to the index page's E(A) in our original example, while all other values E equal 1 and if the damping factor d is 0.85, we get the following BadRank values:

Page A B/C D/E/F/G	BadRank 22.39 17.39 12.21

First of all, we see that the BadRank distributes from the index page among all other pages of the website. The combination of PageRank and BadRank will be discussed in detail below, but, no matter how the combination will be realized, it is obvious that both can neutralize each other very well. After all, we can assume that also the page's PageRank decreases, the lower the hierarchy level is, so that a PR0 can easily be achieved for all pages.

If we now assume that the hierarchically inferior page G links to a page X with a constant BadRank BR(X)=10, whereby the link from page G is the only inbound link for page X, and if all values E for our example website equal 1, we get, at a damping factor d of 0.85, the following values:

Page A B C D E F G	BadRank 4.82 7.50 14.50 4.22 4.22 11.22 17.18

In this case, we see that the distribution of the BadRank is less homogeneous than in the first scenario. Non the less, a distribution of BadRank among all pages of the website takes place. Indeed, the relatively low BadRank of the index page A is remarkable. It could be a problem to neutralize its PageRank which should be higher compared to the rest of the pages. This effect is not really desirable but it reflects the experiences of numerous webmasters. Quite often, we can see the phenomenom that all pages except for the index page of a website show a PR0 in the Google Toolbar, whereby the index page often has a Toolbar PageRank between 2 and 4. Therefore, we can probably assume that this special variant of PR0 is not caused by the detection of the according website by a spam filter, but the site rather received a penalty for "linking to bad neighbourhoods". Indeed, it is also possible that this variant of PR0 occurs when only hierarchical inferior pages of a website get trapped in a spam filter.

11. PR0 - Google's PageRank 0 Penalty (continued)

This article reproduced with permission of eFactory.
© 2002 eFactory Internet-Agentur KG Online-Marketing - written by Markus Sobek
PageRank and Google are trademarks of Google Inc., Mountain ViewCA, USA.
PageRank is protected by US Patent 6,285,999.