This is a file from the Wikimedia Commons

File:PageRanks-Example.svg

From Wikipedia, the free encyclopedia
Jump to: navigation, search
Original file ‎(SVG file, nominally 758 × 611 pixels, file size: 33 KB)
Description

Numeric examples of PageRank values in a small graph with a damping factor of 0.85. The exact solution is:

\mathbf{R} = \begin{bmatrix} PR(A)\\ PR(B)\\ \vdots\\ PR(K) \end{bmatrix} = \dfrac{1}{579662461}\cdot \begin{pmatrix} 19002201\\ 222822800\\ 198772220\\ 22657320\\ 46886400\\ 22657320\\ 9372840\\ 9372840\\ 9372840\\ 9372840\\ 9372840 \end{pmatrix} \approx \begin{pmatrix} 0,03278149\\ 0,38440095\\ 0,34291029\\ 0,03908709\\ 0,08088569\\ 0,03908709\\ 0,01616948\\ 0,01616948\\ 0,01616948\\ 0,01616948\\ 0,01616948 \end{pmatrix}

And here’s the solution for any arbitrary damping factor d:

\mathbf{R_d} = \begin{bmatrix} PR_d(A)\\ PR_d(B)\\ \vdots\\ PR_d(K) \end{bmatrix} =\left(\dfrac{1}{(d+1)\cdot(7\,d^4+28\,d^2+12\,d-132)}\right)\cdot \begin{bmatrix} \left( {d}+1 \right) \left( 7\,{{d}}^{3}+6\,{d}+12\right) \left( {d}-1 \right)\\ -9\,{{d}}^{3}-18\,{{d}}^{2}-46\,{d}-12\\ -11\,{{d}}^{4}-12\,{d}-12-18\,{{d}}^{3}-32\,{{d}}^{2}\\ 2\, \left( {d}+1 \right) \left( 7\,{{d}}^{2}+2\,{d}+6 \right) \left( {d}-1 \right)\\ 12\, \left( {d}+1 \right) \left( 4\,{{d}}^{2}-3\,{d}-1\right)\\ 2\, \left( {d}+1 \right) \left( 7\,{{d}}^{2}+2\,{d}+6 \right) \left( {d}-1 \right)\\ -2\, \left( {d}+1 \right) \left( -6+{{d}}^{2} \right) \left( {d}-1 \right)\\ -2\, \left( {d}+1 \right) \left( -6+{{d}}^{2} \right) \left( {d}-1 \right)\\ -2\, \left( {d}+1 \right) \left( -6+{{d}}^{2} \right) \left( {d}-1 \right)\\ -2\, \left( {d}+1 \right) \left( -6+{{d}}^{2} \right) \left( {d}-1 \right)\\ -2\, \left( {d}+1 \right) \left( -6+{{d}}^{2} \right) \left( {d}-1 \right) \end{bmatrix}
Date 2007-11-25, 2008-01-29
Source en:Image:PageRanks-Example.jpg. Inspired in File:PageRank-hi-res.png.
Author en:User:345Kai, User:Stannered
Permission
(Reusing this file)
Public domain This work has been released into the public domain by its author, 345Kai at English Wikipedia. This applies worldwide.
In some countries this may not be legally possible; if so:
345Kai grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
Other versions

en:Image:PageRanks-Example.jpg, stricter copy of original image
SVG development
W3C icon.svg
 The source code of this SVG is valid.
Inkscape-yes.svg
 This vector image was created with Inkscape.

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current16:17, 8 July 2009Thumbnail for version as of 16:17, 8 July 2009758 × 611 (33 KB)FrakturfreundAdded the procent sign for clarity after a discussion in the german wikipedia.
00:19, 29 January 2008Thumbnail for version as of 00:19, 29 January 2008758 × 611 (33 KB)Stannered{{Information |Description=Numeric examples of PageRanks in a small system. |Source=en:Image:PageRanks-Example.jpg |Date=2007-11-25, 2008-01-29 |Author=en:User:345Kai, User:Stannered |Permission={{PD-user-en|345Kai}} |other_versions=[[:en:Im
The following pages on the English Wikipedia link to this file (pages on other projects are not listed):

Global file usage

The following other wikis use this file:

Retrieved from "https://en.wikipedia.org/wiki/File:PageRanks-Example.svg"