Re: [igraph] PageRank implementations give vastly different results

[Tamás Nepusz]

Hi,

This could be a bug in at least two of the three implementations ;) We cannot 
tell for sure, but if you send me a small(ish) graph for which you think PRPACK 
is wrong, I’ll try to investigate.

FWIW, we’ve had convergence problems with ARPACK in the past so that’s one of 
the reasons why we switched to PRPACK (the other one was efficiency). However, 
it could be the case that there’s either a bug in PRPACK or in the glue code 
between igraph and PRPACK, so it’s definitely worth a closer look.

All the best,
--  
T.

------------------------------------------------------
From: Tim Althoff address@hidden
Reply: Help for igraph users address@hidden
Date: 11 May 2014 at 01:34:38
To: Help for igraph users address@hidden
Subject:  [igraph] PageRank implementations give vastly different results

> Hi,
>  
> I have a graph with about 100k nodes and I'm running personalized pagerank
> from a set of about 100-1000 nodes. I noticed really weird results with the
> standard implementation PRPACK and then started playing around with the
> different implementations.
>  
> PRPACK
> i pr node_index indegree
>  
>  
> 0 0.00621379133505 4236 0
> 1 0.00500739507819 289 185
> 2 0.00403557013917 166 248
> 3 0.00241985179915 231 72
> 4 0.00215338391426 272 81
> 5 0.00214373084523 288 82
> 6 0.00188359270723 4950 0
> 7 0.00184160316546 4269 6
> 8 0.00184074499462 2658 0
> 9 0.00165858327568 228 87
>  
>  
>  
> ARPACK (seems most reasonable but how would I know)
> i pr node_index indegree
>  
>  
> 0 0.0234442644132 289 185
> 1 0.0196580845557 3865 205
> 2 0.0117400740699 166 248
> 3 0.0091531577429 5289 38
> 4 0.00904311638885 288 82
> 5 0.00836828243054 5324 39
> 6 0.00824148456229 350 43
> 7 0.00751007382417 1257 62
> 8 0.00749031863684 1293 52
> 9 0.00734012549007 231 72
>  
>  
>  
> Power (slow)
>  
> i pr node_index indegree
>  
>  
> 0 0.152992115688 356 40
> 1 0.152981241191 6256 3
> 2 0.13547184379 6332 2
> 3 0.124488680058 2736 1
> 4 0.118762538775 1163 2
> 5 0.115458144486 1569 1
> 6 0.115458144486 1551 1
> 7 0.0127839057389 166 248
> 8 0.0109754101098 1097 18
> 9 0.0109437441275 2360 6
>  
>  
>  
> So we find that the PR distribution are very different. Also it seems
> weird that nodes with indegree zero would have such a high pagerank
> (damping=0.85, default). It seems to stop optimizing prematurely.
>  
>  
> If this is just an issue of an "eps" in the optimization routine, how
> can I control this? I found nothing about how to use arpack options
> but it also seemed that the package chose prpack since 0.7. What can I
> do to get result that I can trust?
>  
>  
> Thanks,
>  
> Tim
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