Extremal Dependencies and Rank Correlations in Power Law Networks

We analyze dependencies in complex networks characterized by power laws (Web sample, Wikipedia sample and a preferential attachment graph) using statistical techniques from the extreme value theory and the theory of multivariate regular variation. To the best of our knowledge, this is the first attempt to apply this well developed methodology to comprehensive graph data. The new insights this yields are striking: the three above-mentioned data sets are shown to have a totally different dependence structure between graph parameters, such as in-degree and PageRank. Based on the proposed approach, we suggest a new measure for rank correlations. Unlike most known methods, this measure is especially sensitive to rank permutations for top-ranked nodes. Using the new correlation measure, we demonstrate that the PageRank ranking is not sensitive to moderate changes in the damping factor.