Flow

Predict one scalar per graph: the maximum feasible flow between designated source and sink vertices under the supplied edge capacities.

Unique synthetic graphs are drawn from ER, stochastic-block, power-law-cluster, Newman-Watts-Strogatz, BA, and dual-BA generators. Generator mixtures define easy, medium, and hard distribution shifts.

Edge attributes encode capacities or weights needed by the flow problem, while node information identifies source and sink. The target is the NetworkX reference maximum-flow value.

Each difficulty provides one million 16-node training graphs plus 10,000 validation and 10,000 128-node test graphs. Graph-level MAE is the metric under the fixed 98/1/1 split.

GraphBench omits flow from its 128-to-512-node size study because target magnitude, and therefore raw MAE, scales with network size. Capacity distribution and generator shift must be held fixed when comparing errors.