  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.
