\begin{graph}
   rankdir=LR
   node [shape=plaintext]
   v_1
   v_1 -> v_2 [label=\sqrt{2}+\frac{1}{(x+5)}, color=forestgreen]
   v_2 -> v_3 [label=$S \subseteq \{1,2,3\}^4$]
   v_3 -> v_1 [label=(f \circ g)^{-1}]
\end{graph}

%% note: the fields inside [] are comma-deliminted, so if there are commas inside a label= math expression, easylatex will break up the math expression at the comma; in this case you must put in the dollar signs manually