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Fig. 3 | BMC Bioinformatics

Fig. 3

From: BRANE Cut: biologically-related a priori network enhancement with graph cuts for gene regulatory network inference

Fig. 3

Schematic view of the proposed BRANE Cut method. The initial graph (a) is transformed into an intermediate graph (b) in which a max-flow computation is performed to return an optimal edge labeling x leading to the inferred graph (c). We choose to present the method in its full generality with unscaled weights (i.e. w i,j [ 0,+[, and λ parameters also belong to [ 0,+[. Nodes v 2 and v 3 are TFs, \({\lambda _{\overline {\text {TF}}}}=1\) and λ TF=3. Taking γ=4 implies that v 1, v 2, and v 3 satisfy the regulator coupling property. Vertices v 1 and v 4 are thus affected, leading to the presence of additional edges weighted by ρ 1,2,3=0 and ρ 4,2,3=3, when μ is set to 3. Computing a max-flow in the graph (b) leads to some edge saturation, represented in dashed lines. The values from the source (value 1) and the sink (value 0) are propagated through non saturated paths, thus leading to x 2,4=x 3,4=0

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