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We interpret G with each edge colored by read mappings as a flow network, considering the read volume assigned to every (super-) edge as a flux created by the expression of the underlying supporting transcripts T.Consequently, given an edge the contribution of each transcript  the supporting transcripts to the flux X_e observed along an edge  it is supporting e can be described by a linear equation

The crux of the flux is that an RNA-Seq experiment provides a series of observations on the underlying expression level t_i along the transcript body. Following traditions tradition in transportation problems, we model all of these observations as a system of linear equations by inferring Equation 1 on all . Subsequently, the linear equations spanned by a locus are resolved by the objective function