Graph mining: Laws, generators, and algorithms
ACM Computing Surveys (CSUR)
Characterization of Tail Dependence for In-Degree and PageRank
WAW '09 Proceedings of the 6th International Workshop on Algorithms and Models for the Web-Graph
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We analyze dependencies in power law graph data (Web sample, Wikipedia sample and a preferential attachment graph) using statistical inference for multivariate regular variation. The well developed theory of regular variation is widely applied in extreme value theory, telecommunications and mathematical finance, and it provides a natural mathematical formalism for analyzing dependencies between variables with power laws. However, most of the proposed methods have never been used in the Web graph data mining. The present work fills this gap. The new insights this yields are striking: the three above-mentioned data sets are shown to have a totally different dependence structure between different graph parameters, such as in-degree and PageRank.