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The Web as a graph
, 2000
"... The pages and hyperlinks of the WorldWide Web maybe viewed as nodes and edges in a directed graph. This graph has about a billion nodes today,several billion links, and appears to grow exponentially with time. There are many reasonsmathematical, sociological, and commercialfor studying the e ..."
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Cited by 175 (2 self)
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The pages and hyperlinks of the WorldWide Web maybe viewed as nodes and edges in a directed graph. This graph has about a billion nodes today,several billion links, and appears to grow exponentially with time. There are many reasonsmathematical, sociological, and commercialfor studying the evolution of this graph. We first review a set of algorithms that operate on the Web graph, addressing problems from Web search, automatic community discovery, and classification. We then recall a number of measurements and properties of the Web graph. Noting that traditional random graph models do not explain these observations, we propose a new family of random graph models.
The WebGraph Framework I: Compression Techniques
 In Proc. of the Thirteenth International World Wide Web Conference
, 2003
"... Studying web graphs is often dicult due to their large size. Recently, several proposals have been published about various techniques that allow to store a web graph in memory in a limited space, exploiting the inner redundancies of the web. The WebGraph framework is a suite of codes, algorithms ..."
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Cited by 158 (30 self)
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Studying web graphs is often dicult due to their large size. Recently, several proposals have been published about various techniques that allow to store a web graph in memory in a limited space, exploiting the inner redundancies of the web. The WebGraph framework is a suite of codes, algorithms and tools that aims at making it easy to manipulate large web graphs. This papers presents the compression techniques used in WebGraph, which are centred around referentiation and intervalisation (which in turn are dual to each other).
A survey on pagerank computing
 Internet Mathematics
, 2005
"... 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. T ..."
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Cited by 64 (0 self)
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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.
Graph summarization with bounded error
 In SIGMOD 2008: Proceedings of the 2008 ACM SIGMOD International Conference on Management of data
, 2008
"... We propose a highly compact twopart 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. ..."
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Cited by 37 (5 self)
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We propose a highly compact twopart 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 edgecorrections 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 coarselevel 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.
Compact Representations of Separable Graphs
 In Proceedings of the Annual ACMSIAM Symposium on Discrete Algorithms
, 2003
"... We consider the problem of representing graphs compactly while supporting queries e#ciently. In particular we describe a data structure for representing nvertex unlabeled graphs that satisfy an O(n )separator theorem, c < 1. The structure uses O(n) bits, and supports adjacency and degree queri ..."
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Cited by 36 (11 self)
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We consider the problem of representing graphs compactly while supporting queries e#ciently. In particular we describe a data structure for representing nvertex unlabeled graphs that satisfy an O(n )separator theorem, c < 1. The structure uses O(n) bits, and supports adjacency and degree queries in constant time, and neighbor listing in constant time per neighbor. This generalizes previous results for graphs with constant genus, such as planar graphs.
The Link Database: Fast Access to Graphs of the Web
"... ... graph where URLs are nodes and hyperlinks are directed edges. The Link Database provides fast access to the hyperlinks. To support a wide range of graph algorithms, we find it important to fit the Link Database into memory. In the first version of the Link Database, we achieved this fit by using ..."
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Cited by 35 (2 self)
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... graph where URLs are nodes and hyperlinks are directed edges. The Link Database provides fast access to the hyperlinks. To support a wide range of graph algorithms, we find it important to fit the Link Database into memory. In the first version of the Link Database, we achieved this fit by using machines with lots of memory (8GB), and storing each hyperlink in 32 bits. However, this approach was limited to roughly 100 million Web pages. This paper presents techniques to compress the links to accommodate larger graphs. Our techniques combine wellknown compression methods with methods that depend on the properties of the web graph. The first compression technique takes advantage of the fact that most hyperlinks on most Web pages point to other pages on the same host as the page itself. The second technique takes advantage of the fact that many pages on the same host share hyperlinks, that is, they tend to point to a common set of pages. Together, these techniques reduce space requirements to under 6 bits per link. While (de)compression adds latency to the hyperlink access time, we can still compute the strongly connected components of a 6 billionedge graph in under 20 minutes and run applications such as Kleinberg's HITS in real time. This paper describes our techniques for compressing the Link Database, and provides performance numbers for compression ratios and decompression speed.
On Compressing Social Networks
"... 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 ..."
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Cited by 35 (1 self)
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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 NPhard 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.
Characterization of national Web domains
 ACM Transactions on Internet Technology
, 2005
"... During the last few years, several studies on the characterization of the public Web space of various national domains have been published. The pages of a country are an interesting set for studying the characteristics of the Web, because at the same time these are diverse (as they are written by se ..."
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Cited by 28 (9 self)
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During the last few years, several studies on the characterization of the public Web space of various national domains have been published. The pages of a country are an interesting set for studying the characteristics of the Web, because at the same time these are diverse (as they are written by several authors) and yet rather similar (as they share a common geographical, historical and cultural context). This paper discusses the methodologies used for presenting the results of Web characterization studies, including the granularity at which different aspects are presented, and a separation of concerns between contents, links, and technologies. Based on this, we present a sidebyside comparison of the results of 12 Web characterization studies comprising over 120 million pages from 24 countries. The comparison unveils similarities and differences between the collections, and sheds light on how certain results of a single Web characterization study on a sample may be valid in the context of the full Web.
I/OEfficient Techniques for Computing Pagerank
"... Over the last few years, most major search engines have integrated linkbased ranking techniques in order to provide more accurate search results. One widely known approach is the Pagerank technique, which forms the basis of the Google ranking scheme, and which assigns a global importance measure to ..."
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Cited by 26 (3 self)
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Over the last few years, most major search engines have integrated linkbased ranking techniques in order to provide more accurate search results. One widely known approach is the Pagerank technique, which forms the basis of the Google ranking scheme, and which assigns a global importance measure to each page based on the importance of other pages pointing to it. The main advantage of the Pagerank measure is that it is independent of the query posed by a user
A Fast and Compact Web Graph Representation
"... Compressed graphs representation has become an attractive research topic because of its applications in the manipulation of huge Web graphs in main memory. By far the best current result is the technique by Boldi and Vigna, which takes advantage of several particular properties of Web graphs. In t ..."
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Cited by 17 (12 self)
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Compressed graphs representation has become an attractive research topic because of its applications in the manipulation of huge Web graphs in main memory. By far the best current result is the technique by Boldi and Vigna, which takes advantage of several particular properties of Web graphs. In this paper we show that the same properties can be exploited with a different and elegant technique, built on RePair compression, which achieves about the same space but much faster navigation of the graph. Moreover, the technique has the potential of adapting well to secondary memory. In addition, we introduce an approximate RePair version that works efficiently with limited main memory.