基于边的网络分析：图和超图的曲率
Edge-based analysis of networks: Curvatures of graphs and hypergraphs
摘要：
网络的结构是由关系而不是要素构成的。因此，我们开发了一个系统的方法来分析网络，建模为图或超图，这是基于（超）边的结构特性，而不是顶点。为此，我们利用所谓的网络曲率。这些曲率量化了（超）边的局部结构属性，也就是说，它们与其他边的连接方式以及连接程度。在有向网络的情况下，它们评估它们接收的输入和它们产生的输出，以及它们之间的关系。有了这些工具，我们可以研究生物网络。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。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
