A note on perron vectors for almost regular tournament matrices

Let T be an almost regular tournament matrix of order n with right perron vector w. We show that if the ith row sum of T is (n − 2)/2 and the jth row sum is n/2, then wi < wj. Thus in the round robin competition corresponding to T, the ranking schemes of Kendall and Wei and of Ramanujacharyula agree with the ranking generated by the row sums of T.