  A finite subset $M \subset \mathbb{R}^d$ is basic, if for any function $f
\colon M \to \mathbb{R}$ there exists a collection of functions $f_1, \ldots,
f_d \colon \mathbb{R} \to \mathbb{R}$ such that for each element $(x_1, \ldots,
x_d)\in M$ we have $f(x_1, \ldots, x_d) = f_1(x_1) + \ldots + f_d(x_d)$. For
certain finite sets, we prove a criterion for a set to be basic, and we show
that it cannot be extended to the general case. In addition, we interpret the
above criterion in terms of doubly-weighted graphs and give an estimation for
the number of elements in certain basic and non-basic subsets.
