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Bi and branching networks are two classes of minimal networks often found in the literatures of two-way flow Strict Nash networks. Why so? In this paper, we answer this question by establishing a generalized condition that holds together many models in the literature, and then show that this condition is sufficient to guarantee their common result: every non-empty component of minimal SNN is either a branching or Bi network. This paper, therefore, contributes to the literature by providing a generalization of several existing works in the literature of two-way flow Strict Nash networks.