Asymptotic Behavior of Common Connections in Sparse Random Networks

Random network models generated using sparse exchangeable graphs have provided a mechanism to study wide variety of complex real-life networks. In particular, these help with investigating power-law properties degree distributions, number edges, and other relevant metrics which support the scale-free structure Previous work on such imposes marginal assumption univariate regular variation (e.g., tail) bivariate generating graphex function. this paper, we by functions are multivariate regularly varying. We also focus different metric for our study: distribution common vertices (connections) shared pair vertices. The being high fixed is an indicator original connected. find that connections varying as well, where tail indices governed type function used. Our results verified simulated estimating index parameters.