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)

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.

Other versions

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

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	16:17, 8 July 2009		758×611 (33 KB)	Frakturfreund (Talk \| contribs)	(Added the procent sign for clarity after a discussion in the german wikipedia.)
	00:19, 29 January 2008		758×611 (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)