Forbid Flow to Split in Flow Network

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Is it possible to somehow assert that flows are not allowed to split in flow networks by design? Assume you have a sink $s$ and a incoming flow value of 10. Furthermore you have 3 nodes $v_1, v_2, v_3$. I want to be the incoming flow in each node $v_i$ to be either $0$ or $5$ and nothing in between. Can this be modelled by somehow by designing a suitable network?

Many thanks.

Here is a small sketch of the situation

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Let the flow variable be $x_{ij}$, introduce a binary variable $y_{ij}$, and impose linear constraint $x_{ij}=5y_{ij}$.