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