  In human society, a lot of social phenomena can be concluded into a
mathematical problem called the bipartite matching, one of the most well known
model is the marriage problem proposed by Gale and Shapley. In this article, we
try to find out some intrinsic properties of the ground state of this model and
thus gain more insights and ideas about the matching problem. We apply
Kuhn-Munkres Algorithm to find out the numerical ground state solution of the
system. The simulation result proves the previous theoretical analysis using
replica method. In the result, we also find out the amount of blocking pairs
which can be regarded as a representative of the system stability. Furthermore,
we discover that the connectivity in the bipartite matching problem has a great
impact on the stability of the ground state, and the system will become more
unstable if there were more connections between men and women.
