Accurate estimation of the functional liver remnant is essential for planning safe liver resections. Unintended vessel transections and subsequent perfusion loss may compromise the functional liver remnant and increase the post-operative risk. We present an approach that models portal and hepatic veins as directed graphs to simulate blood flow and predict downstream perfusion loss by cut vessels. Quantitative metrics, including perfused functional liver remnant and spatial mismatch to the planned resection zone, are automatically computed and visualized. We demonstrated on 22 patients and 31 resections zones that in most cases non-perfused regions extended beyond the planned resection zone, indicating potential risk areas for risk stratification. In conclusion, graph-based perfusion modeling provides quantitative and visual feedback to support pre-operative planning of complex liver resections. This approach may aid in identifying high-risk territories and optimizing resection strategies, demonstrating promising value for surgical decision support.