Exercise 6, § 6

Let $G$, $H$ be the graphs of two equivalences on $E$. Then $G \circ H$ is the graph of an equivalence on $E$ if and only if $G \circ H = H \circ G$. The graph $G \circ H$ is then the intersection of all the graphs of equivalences on $E$ which contain both $G$ and $H$.