Extension of the refined convergence-rate bound to regular graphs

Let the simple symmetric case mean the setting in which the relevant communication graph is regular but not necessarily transitive. Let the bound referred to in Theorem be the convergence-rate bound established there.

Regular-graph extension conjecture. The bound given in Theorem remains valid in the simple symmetric case, for example for regular graphs without transitivity.

This conjecture arose from numerical experiments suggesting that the refined bound also applies beyond transitive graphs. Its status is not resolved in the supplied source context.