Linear graphs are used in Taguchi Experimental Designs to help allocate the appropriate columns of a Taguchi array to the factors and interactions. The figures show two alternative linear graphs for the L8 design:
Column 3 contains the interaction between columns 1 and 2.
The circles are coded to distinguish the columns that have many level changes from those with few changes. If it is difficult to change the level of one of the factors, column 1 would be a good choice, and column 4 a poor choice. This would not be a consideration with classical designs because the runs are randomized, but Taguchi experiments are not usually randomized.