Measuring extremal dependencies in Web graphs

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 theory of regular variation is well developed and applied in extreme value theory, telecommunications, and mathematical finance and provides a natural mathematical formalism for analyzing dependencies between variables with power laws. However, most of the proposed methods have never been applied to the Web graph data. This paper 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 Web graph parameters, such as in-degree and PageRank. Additionally, our results confirm the presence of power laws and yields estimates for the power law exponent. The proposed approach to power laws and dependencies enable us to resolve a number of disagreements in the existing literature.