There are many articles on the net about how the PageRank algorithm works that all copy from the original paper written by the very founders of Google Larry Page and Sergey Brin. Google itself also has a very good article that explain it with no formulas or numerical explanations. Basically PageRank is like social networks. If you're mentioned by someone important, your importance increases and the people you mention gets upped as well.

We recently had a coursework in discrete mathematics to calculate PageRank values for all web pages in a web matrix. To be able to do this you have to do many simplifications and you're limited in terms of complexity to keep it possible to do "by hand". I wrote a little program that calculates the PageRank for any web with no simplifications. The outcome is that I can quickly calculate the PageRank values for each page.

Here's how to use it:

from PageRank import PageRanker
web = ((0, 1, 0, 0),
       (0, 0, 1, 0),
       (0, 0, 0, 1),
       (1, 0, 0, 0))

pr = PageRanker(0.85, web)
print pr.getPageRank()

Think of the entries in the matrix as A to D along every row and which page it has a link to along the column. In the above example it means that A has a link to B, B as a link to C, C has a link to D, D has a link to A. Graph 1

The PageRank values when you run 100 iterations with no random jumps is:

[ 0.25  0.25  0.25  0.25 ]

Pretty obvious isn't it. One complication with the PageRank algorithm is that even if every page has an outgoing link, you don't always cover everything by just following links. That's why to sometimes need to random start over again from a randomly selected webpage. This is we we use 8.5 in the above example. That qualitativly means that there's a 15% chance that you randomly start on a random webpage and iterate from there.

Let's have a "more complex" web model:

web = ((0, 1, 0, 0),
       (0, 0, 1, 0),
       (0, 1, 0, 1),
       (1, 1, 0, 0))

Graph 2

Running the algorithm again we find:

[ 0.14285725  0.28571447  0.28571419  0.2857141 ]

Notice how page B has the same PageRank as C and D even though page B has two links coming in to it. This is because it spreads it popularity to other pages. It also matters that the initial guess is that every page is equal initially.

Enough said, download the script yourself and make sure you have Python and the numarray Python module installed.


Post your own comment

Here's another interesting and more applicative pagerank calculator:


bug: the first matrix has two edges for C


Cheers. Fixed it.

George Hotelling

Does Google's patent prevent this from being used in site search engines, like as an addon for ?


I don't know actually. It's such a smart thing that makes you wonder how other search engines would do for sorting.


Here's another pagerank calculator:


The most accurate PageRank Checker (ofcourse, for people without ability to use Google Toolbar) Tool I found is this one:


Here you can get more information about the official Google PageRank checksum (parameter "ch" in the Google Toolbar), needed for requests of the PageRank values. You can test this script with your own domains and can even download it.


Hi there

I have been given the task of getting links for our websites that have good page rank on the links directories.
In addition we have many categories so your site will be place on an appropriate page.

If you would like to trade links please send me your website details.

P.S.: I got your e-mail publicly listed on your webpage . Our apologies if you do not wish to take part in a link exchange.

Best Regards,
Marry Tailor

Peter Bengtsson

no thanks. I'd rather not have a link exchange with an unrelated site. I'm sure google can notice what is going on an suspect spam.

If you're going to have a link exchange, do that with sites that mention similar keywords.


seems to be wrong( to me ).
in _improve shouldn't
invariantmatrix multiply with _linkedmatrix and then add itself to _randmatrix ??


Bug: the program doesn't work when any of the web pages has no outgoing links, i.e. all-zero row in webmatrix.


Dear all
please tell me the no of iteration can be get the accurate result
and i want the example of use the eginevalue to determine the Page Rank


dear all
i want reaal data to compute Page Rank


I want Real Data to compute Page Rank

Wing Wong

Sweet. Got a friend who's doing some python coding at . Guess it'll be a good time to ring him up and maybe setup a test. I tried to download it to run against my site at , but it doesn't work for me. :(


Bug: in the second example B should have better PageRank than the others.


I think there is a bug because in the second example B should have better rank than ther others.
Here is an implementation in pure python without using numaarray and the complete N*N matrix. Enjoy!


thank you


Interesting article.


Nice site - pity you have to go to such lengths to moderate it.
I am from Mexico and also am speaking English, give please true I wrote the following sentence: "It just like any other kind of dating that goes on."

Thank :-) Hector.

Website Hosting India

Thanks for sharing, but we have to install ruby on rails on server

Peter Bengtsson

The install Django instead :)

Zoltan Toth-Czifra

Sorry, the link to the script is broken. Can you restore it please?

Peter Bengtsson

Hi Zoitan, I'm sorry but it was 8 years ago since I wrote that stuff. I'm sure there are some other newer versions available on the web.

Alex Leca

Great post!
I found this web app to predict in real time Google Page Rank based on the original Google algorithm:
Give it a try!

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