We interpret *G* with each edge \(e \in E\) 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 \(e=(tail,head,exonic,T)\) the contribution of the supporting transcripts \(\{t_1,\ldots,t_n\}\in T\) to the flux \(X_e\) observed along e can be described by a linear equation

\(\sum_{t_i\in T_e}(f_i t_i) \pm \Delta_e = X_e\)

(**Equation 1**)

where *f*_{i} represents a factor that expresses the fraction of the respective transcript expression *t*_{i} observed between *tail*_{e} and *head*_{e}. In the trivial case, *f*_{i} corresponds to the proportion of the interval [*tail*_{e};* head*_{e}] in comparison to the entire length of the processed transcript. The correction factor \(\Delta_e\) in Eq.1 is to compensate for divergence from the expectation created by stochastical sampling intrinsic to RNA-Seq experiments.

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 tradition in transportation problems, we model all of these observations as a system of linear equations by inferring Equation 1 on all \(e\in E\). Subsequently, the linear equations spanned by a locus are resolved by the objective function

\(min(\sum_e \Delta_e)\)

(**Equation 2**)

Solving the linear program (Eq.2) imposed by a locus intrinsically provides an estimate for the expression level *t*_{i} of all alternative transcripts that are annotated.