A weighted digraph is a digraph such that every arc is assigned a nonnegative
number, called the weight of the arc. The weighted outdegree of a vertex v in
a weighted digraph D is the sum of the weights of the arcs with v as their
tail, and the weight of a directed cycle C in D is the sum of the weights
of the arcs of C. In this note we prove that if every vertex of a weighted
digraph D with order n has weighted outdegree at least 1, then there exists
a directed cycle in D with weight at least 1/log2n. This proves a
conjecture of Bollob\'{a}s and Scott up to a constant factor