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

Characterizing Complex Networks with Forman-Ricci Curvature and Associated Geometric Flows

Melanie Weber, Emil Saucan and Jürgen Jost


We introduce Forman-Ricci curvature and its corresponding flows as characteristics for complex networks attempting to extend the common approach of node-based network analysis by edge-based characteristics. Following a theoretical introduction and mathematical motivation, we apply the proposed network-analytic methods to static and dynamic complex networks and compare the results with established node-based characteristics. Our work suggests a number of applications for data mining, including denoising and clustering of experimental data, as well as extrapolation of network evolution.

MSC Codes:
05C82, 05C75, 05C21, 05C10
complex networks, Forman-Ricci Curvature, Ricci flow, Laplacian Flow, Data Mining

Related publications

2017 Repository Open Access
Melanie Weber, Emil Saucan and Jürgen Jost

Characterizing complex networks with Forman-Ricci curvature and associated geometric flows

In: Journal of complex networks, 5 (2017) 4, pp. 527-550