Abstract. We present a simple algorithm for computing the PageRank (stationary distribution) of the stochastic Google matrix G. The algorithm lumps all dangling nodes into a single node. We express lumping as a similarity transformation of G, and show that the PageRank of the nondangling nodes can be computed separately from that of the dangling nodes. The algorithm applies the power method onl...

To determine the order in which to display web pages, the search engine Google computes the PageRank vector, whose entries are the PageRanks of the web pages. The PageRank vector is the stationary distribution of a stochastic matrix, the Google matrix. The Google matrix in turn is a convex combination of two stochastic matrices: one matrix represents the link structure of the web graph and a se...

PageRank is defined as the stationary state of a Markov chain. The chain is obtained by perturbing the transition matrix induced by a web graph with a damping factor α that spreads uniformly part of the rank. The choice of α is eminently empirical, and in most cases the original suggestion α = 0.85 by Brin and Page is still used. In this paper, we give a mathematical analysis of PageRank when α...

In 1999, Page et al. described their algorithm — PageRank — for scoring pages in their web search engine, Google. Already from the start it was clear that due to the large number of pages to be ranked, the PageRank algorithm’s efficiency and optimal performance was and is a critical feature. One method of increasing the efficiency of calculations is based on MapReduce, also originally published...

In this paper we explore the use of ranking as a mean of guiding unsupervised image segmentation. Starting by the well known Pagerank algorithm we introduce an extension based on quantum walks. Pagerank (rank) can be used to prioritize the merging of segments embedded in uniform regions (parts of the image with roughly similar appearance statistics). Quantum Pagerank, on the other hand, gives h...

A generalized refined Arnoldi method based on the weighted inner product is presented for computing PageRank. The properties of the generalized refined Arnoldi method were studied. To speed up the convergence performance for computing PageRank, we propose to change the weights adaptively where the weights are calculated based on the current residual corresponding to the approximate PageRank vec...

Google, the largest search engine worldwide, adopts PageRank technology to determine the rank of website listings. This paper describes how damping factor is a critical factor in changing a website’s ranking in traditional Google PageRank technology. A modified algorithm based on input–output ratio concept is proposed to substitute for the damping factor. Besides there is no need to choose an o...

The research community has devoted an increased attention to reduce the computation time needed by Web ranking algorithms. Many efforts have been devoted to improve PageRank [4, 23], the well known ranking algorithm used by Google. The core of PageRank exploits an iterative weight assignment of ranks to the Web pages, until a fixed point is reached. This fixed point turns out to be the (dominan...

The idea for this note arose during the “Web Information Retrieval and Linear Algebra Algorithms” held at Schloss Dagstuhl in February 2007. Many brilliant people working on either side (numerical analysis and web search) had a chance to meet and talk for one week about mathematical and practical aspects of linear methods for ranking, and in particular (not surprisingly) PageRank and HITS. Ther...

The paper introduces a novel algorithm derived from the PageRank algorithm of Brin and Page. The PageRank algorithm interprets an hyperlink from page a to page b as being a positive vote from a to b. Starting from this interpretation, it attributes a rank to each page. However, it does not offer the possibility to take into account negative votes. The PageTrust algorithm includes negative links...