标题： 复制经验度分布的一阶矩和二阶矩 显示英文标题

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

摘要： 对于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。 在这些模型中，指数随机图（ERGs）近年来获得了越来越多的关注。 到目前为止，只有线性ERGs被广泛用于深入了解现实世界复杂网络的结构组织。 然而，没有一个模型能够解释经验度分布的方差。 为此，必须考虑非线性ERGs。 在表明通常的平均场近似会使两星模型的度校正版本退化之后，我们定义了它的一个由适应性引起的变体。 这种“软化”模型能够在纯粹的规范框架内再现样本方差，同时保留其线性对应模型的解释力。 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.