First Order interpretation of arbitrary structures as a graph

Question

I am currently trying to get some intuition on the concept of First Order reductions, and have come across this exercise question by Immerman, dubbed "Everything is a Graph".

Given some arbitrary relational structure $S$ of some vocabulary $\sigma$, show that there are first-order queries $I$ and $I^{-1}$, such that $G:=I(S)$ is a directed graph, and $I^{-1}(G)$ is isomorphic to $S$.

I would be grateful for some hints and proof ideas, as I struggle a bit with seeing how the encoding would work.