FORMAN–RICCI CURVATURE FOR HYPERGRAPHS

Hypergraphs serve as models of complex networks that capture more general structures than binary relations. For graphs, a wide array statistics has been devised to gauge different aspects their structures. lack behind in this respect. The Forman–Ricci curvature is for graphs based on Riemannian geometry, which stresses the relational character vertices network by focusing edges rather vertices. Despite many successful applications measure not introduced hypergraphs. Here, we define directed and undirected hypergraphs such recovered special case. It quantifies trade-off between hyperedge (arc) size degree participation other hyperedges (arcs). determine upper lower bounds both particular. then applied two large networks: Wikipedia vote metabolic bacterium Escherichia coli. In first case, governed hyperedges, while second example, it dominated degree. We found number users involved elections goes hand-in-hand with experienced users. values allowed detecting redundant bottle neck reactions. ADP phosphorylation reaction but reverse similarly central metabolism. Furthermore, show utility quantification assortativity illustrate idea investigating three networks.