Let $A\in \Bbb F^{n\times m}$.
Let $\operatorname{neighborhood}(x)$ denote the elements surrounding $x$ ($x$ included). Let $a,b,c\in A$, $k\in \Bbb F$.
I've come across the following relation:
$$a\mathcal R_kb \iff a^2+\sum_ {c \in\operatorname {neighborhood(a)}}c^2=k.$$ Where $b$ is some element $\in \operatorname{neighborhood}(a)$.
I'm interested in knowing if this relation is an equivalence relation, it's easy to see that the relation is reflexive.