A schematic diagram of the information-flow model with dissipation, saturation and direction for pathway inference. A. Simplified example of the pathway inferring problem. The paths composed of green nodes and edges are the inferred pathway whereas the blue nodes and edges are predicted to be not relevant. The edge thickness denotes the capacity limit of each edge. B. Constraints imposed on the edges and the nodes. B1. The source only sends information flows out. The total amount is given by I0. B2. The information flow dissipates on each edge, illustrated by the thickness of the edge. B3. There is a capacity limit on each edge. B4. The information only flows in the direction of the interactions. B5. The amount of the input flow should not be less than the amount of the output flow at each intermediate node. B6. The target only receives information flows in. The goal is to maximize the total information flow that the target receives.