Networks : Pim van der Hoorn
From Belle Taylor on July 5th, 2021
Name: Pim van der Hoorn
Talk Title: Tails in networks: a tale of finding the right slope.
Abstract: Network science has long been fascinated with studying the tail of the distribution of the degrees of nodes in a network. Early observations that this tail often seemed to behave as a regularly varying function with exponent between 1 and 2, have driven research in inferring these tail-exponents in network data and studying how they impact other network properties. It was however only recently that this problem was properly placed within the framework Extreme-Value Theory. This link has allowed for well-established tools to be applied for analyzing degree distributions and made the problem of tail inference of degrees more mathematically grounded. However, degrees do not have a monopoly on regularly varying behavior in networks. There are many degree dependent structural measures of networks which seem to have regularly varying tails as well. An example of this is the clustering function, which measures for each value k the average fraction of triangles in which nodes with degree k participate. When the degrees have a regularly varying distribution, the tail of this functions decays with the degree as a regularly varying function as well. Here the exponent often depends on specific model parameters and can exhibit interesting phase-transitions. More interestingly, these exponents also exhibit some form of universality. Meaning that they behave similarly for a wide variety of different models. In this talk I will discuss both occurrences of regularly varying tails in networks. I will start by highlighting some interesting developments and new insights regarding the inference of tail-exponents in degree distributions. After that I will introduce several degree-dependent measures and their corresponding tail behavior. My goal is to open a scientific discussion on how to properly analyze such tails and understanding the relation between these and the tails of the degrees.
This is an invited talk at EVA 2021.