We provide a model that bridges the gap between two benchmark models of strategic network formation. Namely, Jackson and Wolinsky’s conections model based on bilateral formation of links, and Bala and Goyal’s two-way flow model, where links can be unilaterally formed. In the model introduced and studied here, a link can be created unilaterally, but when it is only supported by one of the two players the flow through the link suffers a certain decay, while when it is supported by both the flow runs without friction. When the decay in links supported by only one player is maximal (i.e. there is no flow) we have Jackson and Wolinsky’s connections model without decay, while when flow in such links is perfect we have Bala and Goyal’s two-way flow model. We study Nash, strict Nash and pairwise stability for the intermediate models. Joint with Norma Olaizola.