Abstract. This paper serves as a companion or extension to the “Inside PageRank” paper by Bianchini et al. [Bianchini et al. 03]. It is a comprehensive survey of all issues associated with PageRank, covering the basic PageRank model, available and recommended solution methods, storage issues, existence, uniqueness, and convergence properties, possible alterations to the basic model, suggested alternatives to the traditional solution methods, sensitivity and conditioning, and finally the updating problem. We introduce a few new results, provide an extensive reference list, and speculate about exciting areas of future research. 1.

Abstract. This survey reviews the research related to PageRank computing. Components of a PageRank vector serve as authority weights for web pages independent of their textual content, solely based on the hyperlink structure of the web. PageRank is typically used as a web search ranking component. This defines the importance of the model and the data structures that underly PageRank processing. Computing even a single PageRank is a difficult computational task. Computing many PageRanks is a much more complex challenge. Recently, significant effort has been invested in building sets of personalized PageRank vectors. PageRank is also used in many diverse applications other than ranking. We are interested in the theoretical foundations of the PageRank formulation, in the acceleration of PageRank computing, in the effects of particular aspects of web graph structure on the optimal organization of computations, and in PageRank stability. We also review alternative models that lead to authority indices similar to PageRank and the role of such indices in applications other than web search. We also discuss linkbased search personalization and outline some aspects of PageRank infrastructure from associated measures of convergence to link preprocessing. 1.

The rapid growth of the web has been noted and tracked extensively. Recent studies have however documented the dual phenomenon: web pages have small half lives, and thus the web exhibits rapid death as well. Consequently, page creators are faced with an increasingly burdensome task of keeping links up-to-date, and many are falling behind. In addition to just individual pages, collections of pages or even entire neighborhoods of the web exhibit significant decay, rendering them less e#ective as information resources. Such neighborhoods are identified only by frustrated searchers, seeking a way out of these stale neighborhoods, back to more up-to-date sections of the web; measuring the decay of a page purely on the basis of dead links on the page is too naive to reflect this frustration. In this paper we formalize a strong notion of a decay measure and present algorithms for computing it e#ciently. We explore this measure by presenting a number of validations, and use it to identify interesting artifacts on today's web. We then describe a number of applications of such a measure to search engines, web page maintainers, ontologists, and individual users.

Since the publication of Brin and Page’s paper on PageRank, many in the Web community have depended on PageRank for the static (query-independent) ordering of Web pages. We show that we can significantly outperform PageRank using features that are independent of the link structure of the Web. We gain a further boost in accuracy by using data on the frequency at which users visit Web pages. We use RankNet, a ranking machine learning algorithm, to combine these and other static features based on anchor text and domain characteristics. The resulting model achieves a static ranking pairwise accuracy of 67.3 % (vs. 56.7% for PageRank or 50 % for random).

Link analysis algorithms have been extensively used in Web information retrieval. However, current link analysis algorithms generally work on a flat link graph, ignoring the hierarchal structure of the Web graph. They often suffer from two problems: the sparsity of link graph and biased ranking of newly-emerging pages. In this paper, we propose a novel ranking algorithm called Hierarchical Rank as a solution to these two problems, which considers both the hierarchical structure and the link structure of the Web. In this algorithm, Web pages are first aggregated based on their hierarchical structure at directory, host or domain level and link analysis is performed on the aggregated graph. Then, the importance of each node on the aggregated graph is distributed to individual pages belong to the node based on the hierarchical structure. This algorithm allows the importance of linked Web pages to be distributed in the Web page space even when the space is sparse and contains new pages. Experimental results on the.GOV collection of TREC 2003 and 2004 show that hierarchical ranking algorithm consistently outperforms other well-known ranking algorithms, including the PageRank, BlockRank and LayerRank. In addition, experimental results show that link aggregation at the host level is much better than link aggregation at either the domain or directory levels.

In this paper we investigate the convergence of iterative stationary and Krylov subspace methods for the PageRank linear system, including the convergence dependency on teleportation. We demonstrate that linear system iterations converge faster than the simple power method and are less sensitive to the changes in teleportation. In order to perform this study we developed a framework for parallel PageRank computing. We describe the details of the parallel implementation and provide experimental results obtained on a 70-node Beowulf cluster.

PageRank-style (PR) link analyses are a cornerstone of Web search engines and Web mining, but they are computationally expensive. Recently, various techniques have been proposed for speeding up these analyses by distributing the link graph among multiple sites. However, none of these advanced methods is suitable for a fully decentralized PR computation in a peer-to-peer (P2P) network with autonomous peers, where each peer can independently crawl Web fragments according to the user’s thematic interests. In such a setting the graph fragments that different peers have locally available or know about may arbitrarily overlap among peers, creating additional complexity for the PR computation. This paper presents the JXP algorithm for dynamically and collaboratively computing PR scores of Web pages that are arbitrarily distributed in a P2P network. The algorithm runs at every peer, and it works by combining locally computed PR scores with random meetings among the peers in the network. It is scalable as the number of peers on the network grows, and experiments as well as theoretical arguments show that JXP scores converge to the true PR scores that one would obtain by a centralized computation. 1.

PageRank has been widely used as a major factor in search engine ranking systems. However, global link graph information is required when computing PageRank, which causes prohibitive communication cost to achieve accurate results in distributed solution. In this paper, we propose a distributed PageRank computation algorithm based on iterative aggregation-disaggregation (IAD) method with Block Jacobi smoothing. The basic idea is divide-and-conquer. We treat each web site as a node to explore the block structure of hyperlinks. Local PageRank is computed by each node itself and then updated with a low communication cost with a coordinator. We prove the global convergence of the Block Jacobi method and then analyze the communication overhead and major advantages of our algorithm. Experiments on three real web graphs show that our method converges 5–7 times faster than the traditional Power method. We believe our work provides an efficient and practical distributed solution for PageRank on large scale Web graphs.

This document presents the JXP algorithm for dynamically and collaboratively computing PageRank-style authority scores of Web pages distributed in a P2P network. In the architecture that we pursue, every peer crawls and indexes Web fragments at its discretion, driven by the thematic profile or overlay neighborhood of the peer. The JXP algorithm runs at every peer, and is initialized by a local authority computation on the basis of the locally available Web fragment. Peers collaborate by periodically “meeting” with other peers in the network. Whenever two peers meet they exchange their local information and use this new information to improve their local authority scores. Even though only local computations are performed, the JXP scores approximate the global importance of pages in the entire network. The storage demand of each peer is linear in the number of Web pages and the locally stored Web fragment. Experiments show the quality and practical viability of the JXP algorithm. 1.

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 only to the smaller lumped matrix, but the convergence rate is the same as that of the power method applied to the full matrix G. The efficiency of the algorithm increases as the number of dangling nodes increases. We also extend the expression for PageRank and the algorithm to more general Google matrices that have several different dangling node vectors, when it is required to distinguish among different classes of dangling nodes. We also analyze the effect of the dangling node vector on the PageRank, and show that the PageRank of the dangling nodes depends strongly on that of the nondangling nodes but not vice versa. At last we present a Jordan decomposition of the Google matrix for the (theoretical) extreme case when all web pages are dangling nodes.