Abstract: Background and Objective: There is a need to improve the existing combinatorial properties of non-uniqueness, affine resolvable, truly self-complementary, truly self-dual and E-optimality of the Partially Balanced Incomplete Design with two Associate Classes [PBIBD (2)] design SR 36 (D1) due to Clatworthy by constructing a new cyclic [PBIBD(2)] design (D2) using the initial block of design SR 36 and compare based on optimality criteria, concurrence graph and circuits. The objective of this research is to find a combinatorial basis for classifying these two designs for “bestness” in experimentation. Materials and Methods: To achieve this study objective, we constructed a cyclic PBIBD (2) design with t = 8, b = 8, r = 4, k = 4 using initial block 1: (1, 2, 3, 4), provided their concurrence graphs and shortest paths, obtained their A-, D- and E-optimality via their canonical efficiency factors (cef). Results: On the basis of design optimality and connectedness, the A-, D- and E-optimality values and number of shortest/longest paths were obtained, hence able to show that design D1 and D2, are well-connected with D1 having the highest optimality based on A-, D- and E-criteria while D2, has the lowest optimality based on A- , D- and E-criteria. Again, design D1 and D2 were equally optimal based on the numbers of shortest and longest paths. Conclusion: D1 appeared as the best design for experimental purposes when compared with D2, in particular experimenters faced with the problem of testing 8 treatments in blocks of 8, in 4 plots with 4 replications.