The PageRank algorithm, used in the Google search engine, greatly improves the results of Web search by taking into account the link structure of the Web. PageRank assigns to a page a score proportional to the number of times a random surfer would visit that page, if it surfed indefinitely from page to page, following all outlinks from a page with equal probability. We propose to improve PageRa...

PageRank is a widespread model for analysing the relative relevance of nodes within large graphs arising in several applications. In current paper, we present cost-effective Hessenberg-type method built upon Hessenberg process solution difficult problems. The new very competitive with other popular algorithms this field, such as Arnoldi-type methods, especially when damping factor close to $1$ ...

PageRank, a ranking metric for hypertext web pages, has received increased interests. As the Web has grown in size, computing PageRank scores on the whole web using centralized approaches faces challenges in scalability. Distributed systems like peer-to-peer(P2P) networks are employed to speed up PageRank. In a P2P system, each peer crawls web fragments independently. Hence the web fragment on ...

Personalized PageRank expresses link-based page quality around userselected pages in a similar way as PageRank expresses quality over the entire web. Existing personalized PageRank algorithms can, however, serve online queries only for a restricted choice of pages. In this paper we achieve full personalization by a novel algorithm that precomputes a compact database; using this database, it can...

We determine analytically the modulus of the second eigenvalue for the web hyperlink matrix used by Google for computing PageRank. Specifically, we prove the following statement: “For any matrix , where is an row-stochastic matrix, is a nonnegative rank-one row-stochastic matrix, and ! " , the second eigenvalue of has modulus # $&%'#( ) . Furthermore, if has at least two irreducible closed subs...