Perfect-group square clustering conjecture for Cayley graphs

Let $G$ be a perfect group and let $S$ be a generating set subject to the restrictions required for the square clustering coefficient. Write $\square(\operatorname{Cay}(G,S))$ for that coefficient. Perfect-group square clustering conjecture. Then

$$\square(\operatorname{Cay}(G,S))=0.$$

This conjecture is motivated by the observation that all perfect groups in the dataset had directed square clustering coefficient zero, suggesting that the statistic detects their strong non-abelian character. The restrictions on $S$ and the general validity of the claim are not specified here.