This paper brings together analyses of two-way flow Strict Nash networks under exclusive player heterogeneity assumption and exclusive partner heterogeneity assumption studied by Galeotti et al. (2006) and Billand et al. (2011) respectively. We provide a proposition that generalizes the results of thesemodels by stating that: (i) StrictNash network consists of multiple non-empty components as in Galeotti et al. (2006), and (ii) each non-empty component is a branching or $B_i$ network as in Billand et al. (2011). This proposition requires that a restriction on link formation cost, which is called Uniform Partner Ranking, is satisfied.