Monopartite projections of bipartite networks are key tools to model indirect interactions in complex systems. The standard approach to extract informative patterns from these systems is to statistically validate them using a suitable null network model. A popular choice of null model is the configuration model (CM), built by constraining the degrees of the network and randomizing everything else. However different CM formulations exist, depending on how the degree constraints are imposed and for which nodes of the bipartite network. Here we systematically investigate the application of the various CM formulations in filtering the same network, showing that they lead to remarkably different results even when the same statistical threshold is adopted. Rather, more similar results are obtained for the same density of statistically significant links. In particular, we show that a common community structure may emerge in a specific range of density values. Finally, we develop a meta-validation approach, which allows to identify model-specific statistical thresholds for which the signal is strongest, and at the same time to obtain results independent of the way in which the null hypothesis is formulated.

中文翻译：

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双向网络投影的元验证

双向网络的单方投影是在复杂系统中建模间接交互的关键工具。从这些系统中提取信息模式的标准方法是使用适当的空网络模型对它们进行统计验证。无效模型的一种流行选择是配置模型（CM），它是通过限制网络的程度并随机化其他所有事物来构建的。但是，存在不同的CM公式，具体取决于程度约束的施加方式以及二分网络的哪些节点。在这里，我们系统地研究了各种CM公式在过滤同一网络中的应用，表明即使采用相同的统计阈值，它们也会导致截然不同的结果。相反，对于相同密度的统计上有意义的链接，可以获得更相似的结果。特别是，我们表明，在特定的密度值范围内，可能会出现共同的群落结构。最后，我们开发了一种元验证方法，该方法可以识别信号最强的特定于模型的统计阈值，同时获得独立于零假设的方式而得出的结果。