  It is conjectured by Godsil that the relative number of controllable graphs
compared to the total number of simple graphs on n vertices approaches one as n
tends to infinity. We prove that this conjecture is true. More generally, our
methods show that the linear system formed from the pair (W, b) is controllable
for a large class of Wigner random matrices W and deterministic vectors b. The
proof relies on recent advances in Littlewood-Offord theory developed by
Rudelson and Vershynin.
