The web link graph has a nested block structure: the vast majority of hyperlinks link pages on a host to other pages on the same host, and many of those that do not link pages within the same domain. We show how to exploit this structure to speed up the computation of PageRank by a 3-stage algorithm whereby (1) the local PageRanks of pages for each host are computed independently using the link...

The importance of a node in a directed graph can be measured by its PageRank. The PageRank of a node is used in a number of application contexts – including web-page ranking – and can be interpreted as the average portion of time spent at the node by an infinite random walk in the graph. We consider the problem of maximizing the PageRank of a node by selecting some of the edges from a set of ed...

We build up a directed network tracing links from a given integer to its divisors and analyze the properties of the Google matrix of this network. The PageRank vector of this matrix is computed numerically and it is shown that its probability is inversely proportional to the PageRank index thus being similar to the Zipf law and the dependence established for the World Wide Web. The spectrum of ...

The PageRank algorithm enables to rank the nodes of a network through a specific eigenvector of the Google matrix, using a damping parameter α ∈]0, 1[. Using extensive numerical simulations of large web networks, with a special accent on British University networks, we determine numerically and analytically the universal features of PageRank vector at its emergence when α → 1. The whole network...

We propose the PageRank model of opinion formation and investigate its rich properties on real directed networks of Universities of Cambridge and Oxford, LiveJournal and Twitter. In this model the opinion formation of linked electors is weighted with their PageRank probability. We find that the society elite, corresponding to the top PageRank nodes, can impose its opinion to a significant fract...

Web archives like the Internet Archive preserve the evolutionary history of large portions of the Web. Access to them, however, is still via rather limited interfaces – a search functionality is often missing or ignores the time axis. Time-travel search alleviates this shortcoming by enriching keyword queries with a time-context of interest. In order to be effective, time-travel queries require...

Recently, the research community has devoted increased attention to reducing the computational time needed by web ranking algorithms. In particular, many techniques have been proposed to speed up the well-known PageRank algorithm used by Google. This interest is motivated by two dominant factors: (1) the web graph has huge dimensions and is subject to dramatic updates in terms of nodes and link...

In a network, identifying all vertices whose PageRank is more than a given threshold value ∆ is a basic problem that has arisen in Web and social network analyses. In this paper, we develop a nearly optimal, sublinear time, randomized algorithm for a close variant of this problem. When given a directed network G = (V,E), a threshold value ∆, and a positive constant c > 3, with probability 1 − o...

We give algorithms for finding graph clusters and drawing graphs, highlighting local community structure within the context of a larger network. For a given graph G, we use the personalized PageRank vectors to determine a set of clusters, by optimizing the jumping parameter α subject to several cluster variance measures in order to capture the graph structure according to PageRank. We then give...

This article describes how various ranking algorithms have been tested to evaluate researchers based on the data from a digital library called CiteSeer. We apply five well-known ranking methods such as citation counts, HITS, or PageRank and seven other methods derived from PageRank that take into account not only citation but also collaboration information to assess the importance of individual...