Discrete curvature on graphs from the effective resistance*

This article introduces a new approach to discrete curvature based on the concept of effective resistances. We propose nodes and links graph present evidence for their interpretation as curvature. Notably, we find relation number well-established curvatures (Ollivier, Forman, combinatorial curvature) show convergence continuous in case Euclidean random graphs. Being both efficient calculate highly amenable theoretical analysis, these resistance have potential shed light theory its many applications mathematics, network science, data science physics.