  Inspired by a very recent work of A. {\DH}uri\'c, S. Jev{\dj}eni\'c and N.
Stopar, we introduce a new definition of zero-divisor graphs attached to rings,
that includes all of the classical definitions already known in the literature.
We provide an interpretation of such graphs as images of a functor, that we
call zero-divisor functor and which is associated with a family of special
equivalence relations fixed beforehand. We thus recover and generalize many
known results for zero-divisor graphs and provide a framework which might be
useful for further investigations on this topic.
