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WWW '99 Proceedings of the eighth international conference on World Wide Web
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SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
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VLDB '99 Proceedings of the 25th International Conference on Very Large Data Bases
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FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
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Combinatorics, Probability and Computing
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COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
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IEEE/ACM Transactions on Networking (TON)
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SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Degree Distribution of Competition-Induced Preferential Attachment Graphs
Combinatorics, Probability and Computing
Convergence law for random graphs with specified degree sequence
ACM Transactions on Computational Logic (TOCL)
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Journal of Computer and System Sciences - Special issue on FOCS 2003
Preferential deletion in dynamic models of web-like networks
Information Processing Letters
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Random Structures & Algorithms
Workshop on Algorithms and Models for the Web Graph
Algorithms and Models for the Web-Graph
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ACM Transactions on Algorithms (TALG)
A fast algorithm to calculate powers of a Boolean matrix for diameter computation of random graphs
WALCOM'08 Proceedings of the 2nd international conference on Algorithms and computation
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Journal of Computer and System Sciences
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SIAM Journal on Discrete Mathematics
Limits and power laws of models for the web graph and other networked information spaces
CAAN'04 Proceedings of the First international conference on Combinatorial and Algorithmic Aspects of Networking
A survey of models of the web graph
CAAN'04 Proceedings of the First international conference on Combinatorial and Algorithmic Aspects of Networking
Cheap, easy, and massively effective viral marketing in social networks: truth or fiction?
Proceedings of the 23rd ACM conference on Hypertext and social media
Network topology models for multihop wireless networks
ISRN Communications and Networking
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Many massive graphs (such as WWW graphs and Call graphs) share certain universal characteristics which can be described by the so-called the "power law". In this paper, we first briefly survey the history and previous work on power law graphs. Then we give four evolution models for generating power law graphs by adding one node/edge at a time. We show that for any given edge density and desired distributions for in-degrees and out-degrees (not necessarily the same, but adhered to certain general conditions), the resulting graph almost surely satisfy the power law and the in/out-degree conditions. We show that our most general directed and undirected models include nearly all known models as special cases. In addition, we consider another crucial aspect of massive graphs that is called "scale-free" in the sense that the frequency of sampling (w.r.t. the growth rate) is independent of the parameter of the resulting power law graphs. We show that our evolution models generate scale-free power law graphs.