Sorting vector based on pairs of comparisons

Dear All,

This should be a quite established algorithm, but I have been searching
for a couple days already without finding any satisfactory solution.

I have a matrix defining pairs of Smaller-Larger arbitrary character
values, like below

Smaller <- c("ASD", "DFE", "ASD", "SDR", "EDF", "ASD")

Larger <- c("SDR", "EDF", "KLM", "KLM", "SDR", "EDF"

matComp <- cbind(Smaller, Larger)

so that matComp looks like this

      Smaller Larger
[1,] "ASD"   "SDR"
[2,] "DFE"   "EDF"
[3,] "ASD"   "KLM"
[4,] "SDR"   "KLM"
[5,] "EDF"   "SDR"
[6,] "ASD"   "EDF"

This matrix establishes six pairs of "larger than" relationships that
can be used to sort the unique values in the matrix,

 > unique(as.vector(matComp))

[1] "ASD" "DFE" "SDR" "EDF" "KLM"

Specifically, I would like to get this:

sorted <- c("ASD", "DFE", "EDF", "SDR", "KLM")

or, equally valid (my matrix does not have the full information):

sorted <- c("DFE", "ASD", "EDF", "SDR", "KLM")

Preferably, I would get the different combinations of the unique values
that satisfy the "larger than" conditions in the matrix...


I am sure this is a trivial problem, but I could not find any algorithm
to solve it.

Any help would be highly appreciated