Forman-Ricci curvature of tournaments

tournaments are a type of directed graph which have been used to study the geometry of classical flag manifolds. We became interested in this type of graphs because the combinatorial properties of tournaments can be used to study geometric properties of the flag manifolds. [21]introduced the Forman-Ricci curvature for directed and undirected hypergraphs and obtained the curvature for graphs as a particular case. In this work we present the basic ideas about the Forman- Ricci curvature for directed graphs, characterize the parabolic tournaments in terms of Forman-Ricci curvature and calculate the Forman-Ricci curvature for any tournament.