Edge-based analysis of networks: Curvatures of graphs and hypergraphs
Marzieh Eidi, Amirhossein Farzam, Wilmer Leal, Areejit Samal, and Jürgen Jost
Contact the author: Please use for correspondence this email.
Submission date: 30. Oct. 2020
Download full preprint: PDF (1074 kB)
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.