Analysis of ground state in random bipartite matching

Bipartite matching problems emerge in many human social phenomena. In this paper, we study the ground state of the Gale–Shapley model, which is the most popular bipartite matchingmodel.We apply theKuhn–Munkres algorithm to compute the numerical ground state of themodel. For the first time,we obtain the number of blocking pairswhich is ameasure of the system instability. We also show that the number of blocking pairs formed by each person follows a geometric distribution. Furthermore, we study how the connectivity in the bipartite matching problems influences the instability of the ground state.