A Counter-Intuitive Correlation in a Random Tournament

Abstract. Consider a randomly oriented graph G = (V, E) and let a, s and b be three distinct vertices in V . We study the correlation between the events {a → s} and {s → b}. We show that, when G is the complete graph Kn, the correlation is negative for n = 3, zero for n = 4, and that, counter-intuitively, it is positive for n ≥ 5. We also show that the correlation is always negative when G is a cycle, Cn, and negative or zero when G is a tree (or a forest).