Ordinal Ranking for Google's PageRank

Authors:
Rebecca S. Wills;Ilse C. F. Ipsen
Affiliations:
wills@roanoke.edu and http://faculty.roanoke.edu/wills/;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2009

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Abstract

We present computationally efficient criteria that can guarantee correct ordinal ranking of Google's PageRank scores when they are computed with the power method (ordinal ranking of a list consists of assigning an ordinal number to each item in the list). We discuss the tightness of the ranking criteria, and illustrate their effectiveness for top k and bucket ranking. We present a careful implementation of the power method, combined with a roundoff error analysis that is valid for matrix dimensions $n