The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of (hyper)edges, instead of vertices. For that purpose, we utilize so-called network curvatures. These curvatures quantify the local structural properties of (hyper)edges, that is, how, and how well, they are connected to others. In the case of directed networks, they assess the input they receive and the output they produce, and relations between them. With those tools, we can investigate biological networks. As examples, we apply our methods here to protein–protein interaction, transcriptional regulatory and metabolic networks.

构成网络结构的是关系，而不是元素。因此，我们开发了一种系统的网络分析方法，建模为图或超图，该方法基于（超）边而不是顶点的结构特性。为此，我们利用所谓的网络曲率。这些曲率量化了（超）边缘的局部结构属性，即它们如何以及如何与其他边缘连接。在有向网络的情况下，它们评估接收的输入和产生的输出以及它们之间的关系。有了这些工具，我们就可以研究生物网络。作为例子，我们将我们的方法应用于蛋白质-蛋白质相互作用、转录调控和代谢网络。