Filling in pattern designs for incomplete pairwise comparison matrices: (Quasi-)regular graphs with minimal diameter

Pairwise comparisons have become popular in the theory and practice of preference modelling quantification. In case incomplete data, arrangements known are crucial for quality results. We focus on decision problems where set pairwise can be chosen it is designed completely before making process, without any further prior information. The objective this paper to provide recommendations filling patterns comparison matrices based their graph representation. proposed graphs regular quasi-regular ones with minimal diameter (longest shortest path). Regularity means that each item compared others same number times, resulting a kind symmetry. A an odd vertices called quasi-regular, if degree every vertex number, except one whose larger by one. draw attention diameter, which missing from relevant literature, order remain closest direct comparisons. If as low possible (among edges), we decrease cumulated errors caused intermediate long path between two items. Contributions include list containing (quasi-)regular 2 3 up until 24 vertices. Extensive numerical tests show recommended indeed lead better weight vectors various other edges. It also revealed examples neither regularity nor small sufficient its own, both properties needed. Both theorists practitioners utilize results, given several formats appendix: plotted graph, adjacency matrix, edges, ‘Graph6’ code.