The algorithm of pairwise stable networks based on supernetworks

Stability is an important aspect of social network. This paper investigates pairwise stability and it's algorithm with Jackson-Wolinsky rules. By establishing abstract games of network formation with respect to path dominance, representing the path dominance of all feasible networks as a supernetwork, and using the conclusion that the path dominance core is equal to the set of pairwise stability, we give an intuitive algorithm to find pairwise stability network. In the meantime, the paper gives the set of pairwise stability network with four nodes and the algorithm.