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

Discrete curvatures and network analysis

Emil Saucan, Areejit Samal, Melanie Weber and Jürgen Jost


We describe an approach to the analysis of chemical (and other) networks that, in contrast to other schemes, is based on edges rather than vertices, naturally works with directed and weighted edges, extends

to higher dimensional structures like simplicial complexes or hypergraphs, and can draw upon a rich body of theoretical insight from geometry. As the approach is motivated by Riemannian geometry, the

crucial quantity that we work with is called Ricci curvature, although in the present setting, it is of course not a curvature in the ordinary sense, but rather quantifies the divergence properties of edges. In order

to illustrate the method and its potential, we apply it to metabolic and gene co-expression networks and detect some new general features in such networks.


Related publications

2018 Journal Open Access
Emil Saucan, Areejit Samal, Melanie Weber and Jürgen Jost

Discrete curvatures and network analysis

In: Match, 80 (2018) 3, pp. 605-622