

Preprint 34/2017
Discrete curvatures and network analysis
Emil Saucan, Areejit Samal, Melanie Weber, and Jürgen Jost
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Submission date: 29. May. 2017
Pages: 16
published in: Match, 80 (2018) 3, p. 605-622
Bibtex
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Abstract:
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.