File:PageRanks-Example.svg

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PageRanks-Example.svg‎ (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 image)
PD-icon.svg This image has been (or is hereby) released into the public domain by its author, 345Kai at the English Wikipedia project. This applies worldwide.

In case this is not legally possible:
345Kai grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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Other versions en:Image:PageRanks-Example.jpg, stricter copy of original image

File history

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Date/TimeThumbnailDimensionsUserComment
current16:17, 8 July 2009Thumbnail for version as of 16:17, 8 July 2009758×611 (33 KB)Frakturfreund (Talk | contribs) (Added 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 (Talk | contribs) ({{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)

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