Transitive reduction of a cyclic graph. The graphs in (b) and (c) are both transitive reductions of the graph in (a), since all three graphs have the same transitive closure. One can see that edges that do not exist in the original graph may occur in its transitive reductions, like (a,c) in (b) and (c,a) in (c).
Bošnački et al. BMC Bioinformatics 2012 13:281 doi:10.1186/1471-2105-13-281