  Any simple group-grading of a finite dimensional complex algebra induces a
natural family of digraphs. We prove that $|E\circ E^{\text{op}}\cup
E^{\text{op}}\circ E|\geq |E|$ for any digraph $\Gamma =(V,E)$ without parallel
edges, and deduce that for any simple group-grading, the dimension of the
trivial component is maximal.
