Limit theorems for assortativity and clustering in the configuration model with scale-free degrees
Remco van der Hofstad, Pim van der Hoorn, Nelly Litvak, Clara Stegehuis · arXiv (Cornell University) · 2017
We consider Pearson's correlation coefficient in the erased configuration model and the clustering coefficient in both the standard and erased configuration model, with regularly-varying degree distributions having finite mean and infinite variance. We prove limit theorems for all three measures, where the limit is a composition of coupled random variables with stable distributions, whose parameters are related to the tail exponent of the degree distribution. An essential tool for our proofs is a new result for the scaling of the number of removed edges in the erased configuration model with scale-free degree distributions, which is of independent interest.