  We study a class of nonlocal partial differential equations presenting a
tensor-mobility, in space, obtained asymptotically from nonlocal dynamics on
localising infinite graphs. Our strategy relies on the variational structure of
both equations, being a Riemannian and Finslerian gradient flow, respectively.
More precisely, we prove that weak solutions of the nonlocal interaction
equation on graphs converge to weak solutions of the aforementioned class of
nonlocal interaction equation with a tensor-mobility in the Euclidean space.
This highlights an interesting property of the graph, being a potential
space-discretisation for the equation under study.
