We use the terminology of [1]. Let D be a strongly connected digraph on n points and containing m lines, and let A = A(D) be the corresponding adjacency matrix, so that A is an n x n 0-1 matrix containing m unit elements. We recall that A and D are said to be p-cyclic if p is the greatest common divisor of the lengths of all directed cycles of D. Clearly, the larger the value of p, the smaller the value of m must be; in this note we make the latter and related statements precise.