Thank you very much for tracking the code! Unfortunately, that doesn't work 
either. I am also fairly certain that allowing the node to stay at the same 
spot would give that node an unwarranted boost in pagerank, so it is probably 
undesirable.

I do have an interesting result though; when I use "arpack" instead of the 
default "prpack", I get the exact same results as my custom written function. 
In other words, when there are nodes that have no outgoing edges, "prpack" and 
"arpack" do the computation differently.

My problem seems to be solved (as long as there is no reason why "arpack" is 
wrong) but this difference between the two algorithms might be of interest to 
you.

Thank you very much.
Omer
________________________________
From: Tamas Nepusz <nta...@gmail.com>
Sent: Monday, January 27, 2020 4:15 PM
To: Yalcin, Omer Faruk <o...@psu.edu>
Cc: Help for igraph users <igraph-help@nongnu.org>
Subject: Re: [igraph] personalized pagerank computation issue


That being said, after your question, I set the probability of navigating to 
other nodes from a node that has no outbound links to the personalization 
vector. That doesn't reproduce the igraph result either.
There's also a third option: if there are no outbound nodes, stay at the same 
node with probability equal to 1-damping, _or_ navigate to a randomly picked 
node accoding to the persionalization vector with probability equal to damping. 
Sorry for not being too precise here; the thing is that igraph is using an 
external library (PRPACK) to calculate personalized PageRank scores, and I only 
managed to track the code to a point where I am convinced that we are passing 
down two  vectors to PRPACK; one is a uniform vector, and the other one is the 
personalization vector submitted by the user. Based on this, I would assume 
that PRPACK uses the personalization vector when the random walk is reset, and 
the uniform vector for a random teleport (after all, why would PRPACK need two 
vectors if it used the personalization vector for both cases?), but I did not 
manage to track it down further because PRPACK contains at least six different 
solvers, optimized for different use-cases, and I did not manage to figure out 
which one it would use in your particular case. But I'm pretty sure that the 
discrepancy between your results and ours is due to some corner case in the 
handling of sink nodes.

T.
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