Matrix computations (3rd ed.)
The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
Extrapolation methods for accelerating PageRank computations
WWW '03 Proceedings of the 12th international conference on World Wide Web
Search Engine Visibility
Proceedings of the 13th international conference on World Wide Web
A Reordering for the PageRank Problem
SIAM Journal on Scientific Computing
Combating web spam with trustrank
VLDB '04 Proceedings of the Thirtieth international conference on Very large data bases - Volume 30
PageRank Computation, with Special Attention to Dangling Nodes
SIAM Journal on Matrix Analysis and Applications
On computing PageRank via lumping the Google matrix
Journal of Computational and Applied Mathematics
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Hypergraph partitioning for faster parallel pagerank computation
EPEW'05/WS-FM'05 Proceedings of the 2005 international conference on European Performance Engineering, and Web Services and Formal Methods, international conference on Formal Techniques for Computer Systems and Business Processes
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The PageRank algorithm is used today within web information retrieval to provide a content-neutral ranking metric over web pages. It employs power method iterations to solve for the steady-state vector of a DTMC. The defining one-step probability transition matrix of this DTMC is derived from the hyperlink structure of the web and a model of web surfing behaviour which accounts for user bookmarks and memorised URLs. In this paper we look to provide a more accessible, more broadly applicable explanation than has been given in the literature of how to make PageRank calculation more tractable through removal of the dangling-page matrix. This allows web pages without outgoing links to be removed before we employ power method iterations. It also allows decomposition of the problem according to irreducible subcomponents of the original transition matrix. Our explanation also covers a PageRank extension to accommodate TrustRank. In setting out our alternative explanation, we introduce and apply a general linear algebraic theorem which allows us to map homogeneous singular linear systems of index one to inhomogeneous non-singular linear systems with a shared solution vector. As an aside, we show in this paper that irreducibility is not required for PageRank to be well-defined.