An extension of Katai-Iwai procedure to derive balancing and minimum balancing sets of a social system (Q1088610)

\textit{O. Katai} and \textit{S. Iwai}, J. Math. Psychology 18, 140-176 (1978; Zbl 0394.92027), discovered a method to derive balancing sets and minimum balancing sets of a sociogram with planar graph structure. In this paper, we offer a new perspective to apply their method to sociograms with arbitrary graph structures. For this purpose, we use the notion of ''marked intersection multigraph'' of a cycle basis of the underlying graph and the notion of p-balance of a marked graph due to \textit{E. Sampathkumar}, Graph Theory Newsl. 2, 3 (1972).