I think you missed out on (d,a) which is ordered in your diagram, and you should add (a,a), (b,b), (c,c) and (d,d). now just put the ordered pairs in a boolean matrix having 1 if the pairs are in the matrix, and 0 if they are not, this should result in a lower triangular matrix.

(c,b) (c,a) (b,a) (d,b) (d,a) (a,a) (b,b) (c,c) (d,d)

1000

1100

1110

1101