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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 417 (8 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
, 2003
"... 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 301 (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
, 2001
"... 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 ..."
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Cited by 238 (2 self)
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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 Pd of vertices with degree d should obey a power law Pdαd−γ. They obtained γ = 29 ± 01 by experiment and gave a simple heuristic argument suggesting that γ = 3. Here we obtain Pd asymptotically for all d ≤ n1/15, 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 178 (1 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.
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 104 (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.
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 100 (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...
Directed ScaleFree Graphs
"... We introduce a model for directed scalefree graphs that grow with preferential attachment depending in a natural way on the in and outdegrees. We show that the resulting in and outdegree distributions are power laws with different exponents, reproducing observed properties of the worldwide web. ..."
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Cited by 71 (5 self)
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We introduce a model for directed scalefree graphs that grow with preferential attachment depending in a natural way on the in and outdegrees. We show that the resulting in and outdegree distributions are power laws with different exponents, reproducing observed properties of the worldwide web. We also derive exponents for the distribution of in (out) degrees among vertices with fixed out (in) degree. We conclude by suggesting a corresponding model with hidden variables.
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 33 (16 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.