This study uses experimental data of pore-scale foam flow inside a high-complexity network to fit a graph-based model describing preferential flow paths using microstructural characteristics of the porous medium. Two experiments, with equal gas fractions but varying injection rates, are modeled in parallel. Proposed paths are solution paths to the k-Shortest Paths with Limited Overlap (k-SPwLO) problem, applied to a graph representation of the porous medium with edge weights representing local throat properties. A 1-parameter model based on throat radius only is tested before integrating a second parameter, describing the alignment of the pores surrounding the throat with respect to the injection pressure gradient. The preferential paths observed in both experiments differ in quantity and with respect to the specific porous zones used. As such, the best fit preferential path models for either experiment show different dependencies on the microstructural parameters. The optimized model for the high injection rate experiment markedly shows a dependence on the pore alignment with pressure gradient as well as throat size, whereas the lower injection rate experiment was best fitted to a model that only includes the throat radius. Overall, the graph-based framework was able to capture many high-flow zones in various model parameter combinations, perhaps as consequence of the relatively spiked throat size distribution of the model.