Computing the Ricci-Flatness of Graphs and Steinerberger Curvature

The notion of Ricci flat graphs was introduced in 1996 by Chung and Yau in connection to a logarithmic Harnack inequality. I will show that self-centred Ollivier-Ricci Bonnet-Myers graphs are Ricci-Flat and discuss the use of Prolog to obtain these results. I will then show the two notions of curvature added to the Graphing Calculator and prove a result for Steinerberger curvature on trees.