Scale-free networks: improved inference

The power-law distribution plays a crucial role in complex networks as well as various applied sciences. Investigating whether the degree distribution of a network follows a power-law distribution is an important concern. The commonly used inferential methods for estimating the model parameters often yield biased estimates, which can lead to the rejection of the hypothesis that a model conforms to a power-law. In this paper, we discuss improved methods that utilize Bayesian inference to obtain accurate estimates and precise credibility intervals. The inferential methods are derived for both continuous and discrete distributions. These methods reveal that objective Bayesian approaches return nearly unbiased estimates for the parameters of both models. Notably, in the continuous case, we identify an explicit posterior distribution. This work enhances the power of goodness-of-fit tests, enabling us to accurately discern whether a network or any other dataset adheres to a power-law distribution. We apply the proposed approach to fit degree distributions for more than 5,000 synthetic networks and over 3,000 real networks. The results indicate that our method is more suitable in practice, as it yields a frequency of acceptance close to the specified nominal level.