MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Edge-based analysis of networks: Curvatures of graphs and hypergraphs

Marzieh Eidi, Amirhossein Farzam, Wilmer Leal, Areejit Samal and Jürgen Jost


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.

Oct 30, 2020
Oct 30, 2020

Related publications

2020 Journal Open Access
Marzieh Eidi, Amirhossein Farzam, Wilmer Leal, Areejit Samal and Jürgen Jost

Edge-based analysis of networks : curvatures of graphs and hypergraphs

In: Theory in biosciences, 139 (2020) 4, pp. 337-348