A Weighted-Graph Curvature Calculator and Whether the Discrete Curvature Senses the Smooth One
Abstract
We investigate whether there is a relationship between the discrete Bakry-\'Emery curvature of a graph and the smooth curvature of an ambient surface into which the graph is embedded geodesically. As we used weighted graphs as test objects, we developed a program for the calculation of the discrete curvature and with the help of this calculator, we observed some indications of such a relationship.
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