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A Brief History of Generative Models for Power Law and Lognormal Distributions
 INTERNET MATHEMATICS
"... Recently, I became interested in a current debate over whether file size distributions are best modelled by a power law distribution or a a lognormal distribution. In trying ..."
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Cited by 257 (7 self)
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Recently, I became interested in a current debate over whether file size distributions are best modelled by a power law distribution or a a lognormal distribution. In trying
Graph structure in the Web
 In Proceedings of the 9th International World Wide Web conference on Computer Networks: The International Journal of Computer and Telecommunications Networking
, 2000
"... The study of the web as a graph is not only fascinating in its own right, but also yields valuable insight into web algorithms for crawling, searching and community discovery, and the sociological phenomena which characterize its evolution. We report on experiments on local and global properties of ..."
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Cited by 223 (7 self)
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The study of the web as a graph is not only fascinating in its own right, but also yields valuable insight into web algorithms for crawling, searching and community discovery, and the sociological phenomena which characterize its evolution. We report on experiments on local and global properties of the web graph using two Altavista crawls each with over 200 million pages and 1.5 billion links. Our study indicates that the macroscopic structure of the web is considerably more intricate than suggested by earlier experiments on a smaller scale.
The degree sequence of a scalefree random graph process. Random Structures and Algorithms
, 2001
"... ABSTRACT: Recently, Barabási and Albert [2] suggested modeling complex realworld networks such as the worldwide web as follows:consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number of earlier vertices, selected with probabilities proport ..."
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Cited by 160 (3 self)
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ABSTRACT: Recently, Barabási and Albert [2] suggested modeling complex realworld networks such as the worldwide web as follows:consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number of earlier vertices, selected with probabilities proportional to their degrees. In [2] and, with Jeong, in [3], Barabási and Albert suggested that after many steps the proportion P�d � of vertices with degree d should obey a power law P�d � α d −γ. They obtained γ = 2�9 ± 0�1 by experiment and gave a simple heuristic argument suggesting that γ = 3. Here we obtain P�d � asymptotically for all d ≤ n 1/15, where n is the number of vertices, proving as a consequence that γ = 3.
Heuristically optimized tradeoffs: a new paradigm for power laws in the internet
, 2002
"... Abstract We give a plausible explanation of the power law distributions of degrees observed in the graphs arising in the Internet topology [5] based on a toy model of Internet growth in which two objectives are optimized simultaneously: "last mile " connection costs, and transmissi ..."
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Cited by 154 (2 self)
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Abstract We give a plausible explanation of the power law distributions of degrees observed in the graphs arising in the Internet topology [5] based on a toy model of Internet growth in which two objectives are optimized simultaneously: &quot;last mile &quot; connection costs, and transmission delays measured in hops. We also point out a similar phenomenon, anticipated in [2], in the distribution of file sizes. Our results seem to suggest that power laws tend to arise as a result of complex, multiobjective optimization.
Generating Network Topologies That Obey Power Laws
 In GLOBECOM
, 2000
"... Recent studies have shown that Internet graphs and other network systems follow powerlaws. Do artificial network topologies commonly used in network simulation studies obey these powerlaws? In this paper we show that current topology generators do not obey all of the powerlaws, and we present two ..."
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Cited by 86 (0 self)
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Recent studies have shown that Internet graphs and other network systems follow powerlaws. Do artificial network topologies commonly used in network simulation studies obey these powerlaws? In this paper we show that current topology generators do not obey all of the powerlaws, and we present two new topology generators that do. Finally, we reevaluate a multicast study to demonstrate the impact of powerlaw topologies. 1 Introduction Recent studies have shown that Internet graphs follow power laws [5]i.e., certain graph metrics follow the distribution y / x ff . This phenomenon has been observed in router topology, interdomain topology [5], and the worldwideweb [1, 2, 6, 7, 8]. Previous metrics used to characterize Internet graphs have focussed on averages: for example, average outdegree of routers. While these metrics are important, they do not capture higherorder properties such as the powerlaws. Network studies often simulate artificial network topologies to evalua...
Towards Compressing Web Graphs
 In Proc. of the IEEE Data Compression Conference (DCC
, 2000
"... In this paper, we consider the problem of compressing graphs of the link structure of the World Wide Web. We provide efficient algorithms for such compression that are motivated by recently proposed random graph models for describing the Web. ..."
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Cited by 81 (1 self)
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In this paper, we consider the problem of compressing graphs of the link structure of the World Wide Web. We provide efficient algorithms for such compression that are motivated by recently proposed random graph models for describing the Web.
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.
World Wide Web: A graphtheoretic perspective
, 2001
"... The World Wide Web can be modeled as a directed graph in which a node represents a Web page and an edge represents a hyperlink. Currently, the number of nodes in this gigantic Web graph is estimated to be over four billion, and is growing at more than seven million nodes a day ⎯ without any centrali ..."
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Cited by 6 (0 self)
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The World Wide Web can be modeled as a directed graph in which a node represents a Web page and an edge represents a hyperlink. Currently, the number of nodes in this gigantic Web graph is estimated to be over four billion, and is growing at more than seven million nodes a day ⎯ without any centralized control. Recent studies suggest that despite its chaotic appearance, the Web is a highly structured digraph, in a statistical sense. The study of this graph can provide insight into Web algorithms for crawling, searching, and ranking Web resources. Knowledge of the graphtheoretic structure of the Web graph can be exploited for attaining efficiency and comprehensiveness in Web navigation as well as enhancing Web tools, e.g., better search engines and intelligent agents. In this proposal, we discuss various problems to be explored for understanding the structure of the WWW. Many research directions are identified such as Web caching, prevention of