  We address the issue of the proximity of interacting diffusion models on
large graphs with a uniform degree property and a corresponding mean field
model, i.e. a model on the complete graph with a suitably renormalized
interaction parameter. Examples include Erd\H{o}s-R\'enyi graphs with edge
probability $p_n$, $n$ is the number of vertices, such that $\lim_{n \to
\infty}p_n n= \infty$. The purpose of this note it twofold: (1) to establish
this proximity on finite time horizon, by exploiting the fact that both systems
are accurately described by a Fokker-Planck PDE (or, equivalently, by a
nonlinear diffusion process) in the $n=\infty$ limit; (2) to remark that in
reality this result is unsatisfactory when it comes to applying it to systems
with $N$ large but finite, for example the values of $N$ that can be reached in
simulations or that correspond to the typical number of interacting units in a
biological system.
