Multivariate heavy tails in complex networks

It has been shown that many real networks are not only “scale-free” (i.e., having a power-law degree distribution), but also contain more complex structures such as “hierarchy” or “self-similarity” that cannot be captured by the preferential attachment random network model. These observations have led to a number of more sophisticated models being proposed in the literature. In this paper we advocate a multivariate analysis perspective based on the notion of MRVs as a unifying framework to study complex structures in networks. We demonstrate the existence of “multivariate heavy tails” in existing network models and real networks, and argue that they better capture the “hierarchical” or “self-similar” structures in these networks.