transitive.reduction in nem does not always return the transitive reduction unless one applies transitive.reduction on the transitive closure of the graph. So I think that either the code should be fixed (by using transitive.closure first) or the documentation fixed (but this second route seems dangerous for those who do not read the help carefully).  This bug will probably also affect rBiopaxParser (its transitiveReduction function).

Examples below taken from discussion and comments in http://stackoverflow.com/a/6702198  as well as comments to  http://stackoverflow.com/a/2372202

library(nem)
m1 <- matrix(0, nrow = 4, ncol = 4)
colnames(m1) <- rownames(m1) <- LETTERS[1:4]
m1[rbind(c(1, 2),
         c(2, 3),
         c(3, 4),
         c(1, 4))] <- 1

## Wrong, since A connected to D directly and through B-> C
nem::transitive.reduction(m1)
## OK
nem::transitive.reduction(transitive.closure(m1))

m2 <- matrix(0, nrow = 4, ncol = 4)
colnames(m2) <- rownames(m2) <- LETTERS[1:4]
m2[rbind(c(1, 2),
         c(2, 3),
         c(3, 4),
         c(1, 3),
         c(1, 4))] <- 1

## Wrong, since A connected to D directly and through B-> C
nem::transitive.reduction(m2)
## OK
nem::transitive.reduction(transitive.closure(m2))