We describe a reordering particularly suited to the PageRank problem, which reduces the computation of the PageRank vector to that of solving a much smaller system and then using forward substitution to get the full solution vector. We compare the theoretical rates of convergence of the original PageRank algorithm to that of the new reordered PageRank algorithm, showing that the new algorithm c...

The efficiency of the PageRank computation is important since the constantly evolving nature of the Web requires this computation to be repeated many times. PageRank computation includes repeated iterative sparse matrix-vector multiplications. Due to the enourmous size of the Web matrix to be multiplied, PageRank computations are usually carried out on parallel systems. Graph and hypergraph par...

The three results on the PageRank vector are preliminary but shed light on the eigenstructure of a PageRank modified Markov chain and what happens when changing the teleportation parameter in the PageRank model. Computations with the derivative of the PageRank vector with respect to the teleportation parameter show predictive ability and identify an interesting set of pages from Wikipedia.

objectives: the current study aimed to first assess the quality, popularity and importance of websites providing persian health-related information, and second to evaluate the correlation of the popularity and importance ranking with quality score on the internet. materials and methods: the sample websites were identified by entering the health-related keywords into four most popular search eng...

We study the impact of collusion –nepotistic linking– in a Web graph in terms of Pagerank. We prove a bound on the Pagerank increase that depends both on the reset probability of the random walk ε and on the original Pagerank of the colluding set. In particular, due to the power law distribution of Pagerank, we show that highly-ranked Web sites do not benefit that much from collusion.

Spammers intend to increase the PageRank of certain spam pages by creating a large number of links pointing to them. We propose a novel method based on the concept of personalized PageRank that detects pages with an undeserved high PageRank value without the need of any kind of white or blacklists or other means of human intervention. We assume that spammed pages have a biased distribution of p...

PageRank is the algorithm used by the Google search engine for ranking web pages. PageRank Algorithm calculates for each page a relative importance score which can be interpreted as the frequency of how often a page is visited by a surfer. The purpose of this work is to provide a mathematical analysis of the PageRank Algorithm. We analyze the random surfer model and the linear algebra behind it...