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 Personalized PageRank expresses backlink-based page quality around user-selected pages in a similar way as PageRank expresses quality over the entire Web. Existing personalized PageRank algorithms can however serve on-line queries only for a restricted choice of page selection. In this paper we achieve full personalization by a novel algorithm that computes a compact database of simulated random walks; this database can serve arbitrary personal choices of small subsets of web pages. We prove that for a fixed error probability, the size of our database is linear in the number of web pages. We justify our estimation approach by asymptotic worst-case lower bounds; we show that exact personalized PageRank values can only be obtained from a database of quadratic size. 1

Web spam can significantly deteriorate the quality of search engine results. Thus there is a large incentive for commercial search engines to detect spam pages efficiently and accurately. In this paper we present a spam detection system that uses the topology of the Web graph by exploiting the link dependencies among the Web pages, and the content of the pages themselves. We find that linked hosts tend to belong to the same class: either both are spam or both are non-spam. We demonstrate three methods of incorporating the Web graph topology into the predictions obtained by our base classifier: (i) clustering the host graph, and assigning the label of all hosts in the cluster by majority vote, (ii) propagating the predicted labels to neighboring hosts, and (iii) using the predicted labels of neighboring hosts as new features and retraining the classifier. The result is an accurate system for detecting Web spam that can be applied in practice to large-scale Web data.

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.

We describe the WEBSPAM-UK2006 collection, a large set of Web pages that have been manually annotated with labels indicating if the hosts are include Web spam aspects or not. This is the first publicly available Web spam collection that includes page contents and links, and that has been labelled by a large and diverse set of judges. 1

PageRank is defined as the stationary state of a Markov chain. The chain is obtained by perturbing the transition matrix induced by a web graph with a damping factor # that spreads uniformly part of the rank. The choice of # is eminently empirical, and in most cases the original suggestion # = 0.85 by Brin and Page is still used. Recently, however, the behaviour of PageRank with respect to changes in # was discovered to be useful in link-spam detection [21]. Moreover, an analytical justification of the value chosen for # is still missing. In this paper, we give the first mathematical analysis of PageRank when # changes. In particular, we show that, contrarily to popular belief, for real-world graphs values of # close to 1 do not give a more meaningful ranking. Then, we give closed-form formulae for PageRank derivatives of any order, and an extension of the Power Method that approximates them with convergence O for the k-th derivative. Finally, we show a tight connection between iterated computation and analytical behaviour by proving that the k-th iteration of the Power Method gives exactly the PageRank value obtained using a Maclaurin polynomial of degree k. The latter result paves the way towards the application of analytical methods to the study of PageRank.

We propose a highly compact two-part representation of a given graph G consisting of a graph summary and a set of corrections. The graph summary is an aggregate graph in which each node corresponds to a set of nodes in G, and each edge represents the edges between all pair of nodes in the two sets. On the other hand, the corrections portion specifies the list of edge-corrections that should be applied to the summary to recreate G. Our representations allow for both lossless and lossy graph compression with bounds on the introduced error. Further, in combination with the MDL principle, they yield highly intuitive coarse-level summaries of the input graph G. We develop algorithms to construct highly compressed graph representations with small sizes and guaranteed accuracy, and validate our approach through an extensive set of experiments with multiple reallife graph data sets. To the best of our knowledge, this is the first work to compute graph summaries using the MDL principle, and use the summaries (along with corrections) to compress graphs with bounded error.

Motivated by structural properties of the Web graph that support efficient data structures for in memory adjacency queries, we study the extent to which a large network can be compressed. Boldi and Vigna (WWW 2004), showed that Web graphs can be compressed down to three bits of storage per edge; we study the compressibility of social networks where again adjacency queries are a fundamental primitive. To this end, we propose simple combinatorial formulations that encapsulate efficient compressibility of graphs. We show that some of the problems are NP-hard yet admit effective heuristics, some of which can exploit properties of social networks such as link reciprocity. Our extensive experiments show that social networks and the Web graph exhibit vastly different compressibility characteristics.

The query-flow graph [Boldi et al., CIKM 2008] is an aggregated representation of the latent querying behavior contained in a query log. Intuitively, in the query-flow graph a directed edge from query qi to query qj means that the two queries are likely to be part of the same search mission. Any path over the query-flow graph may be seen as a possible search task, whose likelihood is given by the strength of the edges along the path. An edge (qi, qj) is also labelled with some information: e.g., the probability that user moves from qi to qj, or the type of the transition, for instance, the fact that qj is a specialization of qi. In this paper we propose, and experimentally study, query recommendations based on short random walks on the queryflow graph. Our experiments show that these methods can match in precision, and often improve, recommendations based on query-click graphs, without using users ’ clicks. Our experiments also show that it is important to consider transition-type labels on edges for having good quality recommendations. Finally, one feature that we had in mind while devising our methods was that of providing diverse sets of recommendations: the experimentation that we conducted provides encouraging results in this sense. 1.

Graphs are widely used to model real world objects and their relationships, and large graph datasets are common in many application domains. To understand the underlying characteristics of large graphs, graph summarization techniques are critical. However, existing graph summarization methods are mostly statistical (studying statistics such as degree distributions, hop-plots and clustering coefficients). These statistical methods are very useful, but the resolutions of the summaries are hard to control. In this paper, we introduce two database-style operations to summarize graphs. Like the OLAP-style aggregation methods that allow users to drill-down or roll-up to control the resolution of summarization, our methods provide an analogous functionality for large graph datasets. The first operation, called SNAP, produces a summary graph by grouping nodes based on user-selected node attributes and relationships. The second operation, called k-SNAP, further allows users to control the resolutions of summaries and provides the “drill-down ” and “roll-up ” abilities to navigate through summaries with different resolutions. We propose an efficient algorithm to evaluate the SNAP operation. In addition, we prove that the k-SNAP computation is NPcomplete. We propose two heuristic methods to approximate the k-SNAP results. Through extensive experiments on a variety of real and synthetic datasets, we demonstrate the effectiveness and efficiency of the proposed methods.