Jackson and Watts [J. of Econ. Theory 71 (2002), 44-74] have examined the dynamic formation and stochastic evolution of networks. We provide a refinement of pairwise stability, pโˆ’pairwise stability, which allows us to characterize the stochastically stable networks without requiring the “tree construction” and the computation of resistance that may be quite complex. When a 1/2โˆ’pairwise stable network exists, it is unique and it coincides with the unique stochastically stable network. To solve the inexistence problem of pโˆ’pairwise stable networks, we define its set-valued extension with the notion of pโˆ’pairwise stable set. The 1/2โˆ’pairwise stable set exists and is unique. Any stochastically stable network is included in the 1/2โˆ’pairwise stable set. Thus, any network outside the 1/2โˆ’pairwise stable set must be considered as a nonrobust network. We also show that the 1/2โˆ’pairwise stable set can contain no pairwise stable network and we provide examples where a set of networks is more “stable” than a pairwise stable network.