论文标题
基于边缘的网络分析：图和超图的曲率
Edge-based analysis of networks: Curvatures of graphs and hypergraphs
论文作者
论文摘要
关系而不是元素构成网络的结构。因此，我们开发了一种系统的方法，以基于（超）边缘的结构属性而不是顶点的结构属性，以模型为图形或超图。为此，我们利用所谓的网络曲率。这些曲率量化了（超）边缘的局部结构特性，即，它们如何以及它们与他人的联系很好。在有导网络的情况下，他们评估收到的输入以及产生的输出以及它们之间的关系。使用这些工具，我们可以研究生物网络。作为示例，我们将这里的方法应用于蛋白质 - 蛋白质相互作用，转录调节和代谢网络。
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.
