A curious phenomenon when it comes to solving the linear system formulation of the PageRank problem is that while the convergence rate of Gauss–Seidel shows an improvement over Jacobi by a factor of approximately two, successive overrelaxation (SOR) does not seem to offer a meaningful improvement over Gauss–Seidel. This has been observed experimentally and noted in the literature, but to the be...

In this paper, we first extend the celebrated PageRank modification to a higher-order Markov chain. Although this system has attractive theoretical properties, it is computationally intractable for many interesting problems. We next study a computationally tractable approximation to the higher-order PageRank vector that involves a system of polynomial equations called multilinear PageRank. This...

In this paper, we propose a new ranking method inspired from previous results on the diffusion approach to solve linear equation. We describe new mathematical equations corresponding to this method and show through experimental results the potential computational gain. This ranking method is also compared to the well known PageRank model. Keywords-Large sparse matrix, Iteration, Fixed point, Pa...

Measures based on the Link Recommendation Assumption are hypothesised to help modern Web search engines rank ‘important, high quality’ pages ahead of relevant but less valuable pages and to reject ‘spam’. We tested these hypotheses using inlink counts and PageRank scores readily obtainable from search engines Google and Fast. We found that the average Google-reported PageRank of websites operat...

As the web is escalating day by day, so people rely on the search engines to investigate the web. In this situation, the challenge for website owner is to provide relevant information to the users as per their needs and fulfill their requirements. The famous search engine Google used Hyperlink structure for ranking the web pages. There are various ranking algorithms are present for getting the ...

Personalized search has gained great popularity to improve search effectiveness in recent years. The objective of personalized search is to provide users with information tailored to their individual contexts. We propose to personalize Web search based on features extracted from hyperlinks, such as anchor terms or URL tokens. Our methodology personalizes PageRank vectors by weighting links base...

Originally, hyperlinks on the web were placed for organic reasons, presumably to aid navigation or identify a resource deemed relevant by the human author. However, link-based reputation measures used by search engines (e.g., PageRank) have altered the dynamics of link-placement by introducing new incentives into the system. Strategic authors — spammers and others — now explicitly attempt to bo...

Traditional link analysis approaches assume equal weights assigned to different links and pages. In original PageRank formulation, the user model assumes that the user has equal probability to follow each link from a given page, thus the score of a page equally affects all of the pages it points to. It also assumes that the probability for a user to go to a URL directly without following a link...

Eigenvector based methods in general, and Google’s PageRank algorithm for rating web pages in particular, have become an important component of information retrieval on the Web. In this paper, we study the efficacy of, and countermeasures for, collusions designed to improve user rating in such systems. We define a metric, called the amplification factor, which captures the amount of PageRank-in...

A network approach, which simplifies geographic settings as a form of nodes and links, emphasizes the connectivity and relationships of spatial features. Topological networks of spatial features are used to explore geographical connectivity and structures. The PageRank algorithm, a network metric, is often used to help identify important locations where people or automobiles concentrate in the ...