标题： 重现经验度分布的一阶和二阶矩 显示英文标题

标题： Reproducing the first and second moment of empirical degree distributions

摘要： 对复杂网络分析的概率模型的研究代表了一个蓬勃发展的研究领域。其中，指数随机图（ERG）多年来引起了越来越多的关注。到目前为止，只有线性ERG被广泛用于深入了解真实世界复杂网络的结构组织。然而，没有一个能够解释经验度分布的方差。为此，必须考虑非线性ERG。在表明通常的平均场近似迫使二星模型的度矫正版本退化后，我们定义了它的以适应度为基础的变体。这个‘软化’模型能够在纯典范框架内再现样本方差，同时保留其线性对应物的解释能力。 显示英文摘要

摘要： The study of probabilistic models for the analysis of complex networks represents a flourishing research field. Among the former, Exponential Random Graphs (ERGs) have gained increasing attention over the years. So far, only linear ERGs have been extensively employed to gain insight into the structural organisation of real-world complex networks. None, however, is capable of accounting for the variance of the empirical degree distribution. To this aim, non-linear ERGs must be considered. After showing that the usual mean-field approximation forces the degree-corrected version of the two-star model to degenerate, we define a fitness-induced variant of it. Such a `softened' model is capable of reproducing the sample variance, while retaining the explanatory power of its linear counterpart, within a purely canonical framework.