  Devriendt and Lambiotte recently introduced the \emph{node resistance
curvature}, a notion of graph curvature based on the effective resistance
matrix. In this paper, we begin the study of the behavior of the node
resistance curvature under the operation of the Cartesian graph product. We
study the natural question of global positivity of node resistance curvature of
the Cartesian product of positively-curved graphs, and prove that, whenever
$m,n\ge3$, the node resistance curvature of the interior vertices of a $m\times
n$ grid is always nonpositive, while it is always nonnegative on the boundary
of such grids. For completeness, we also prove a number of results on node
resistance curvature in $2\times n$ grids and exhibit a counterexample to a
generalization. We also give generic bounds and suggest several further
questions for future study.
