Capacity Counts: Learning to Predict Hyperedges

Hyperedge prediction scores a candidate node set from observed group interactions. Historical hyperedges may repeatedly rely on the same members, so their count can overstate the support that admits distinct representatives. We introduce CapacityDegree, which represents this assignable support through capacity-constrained matching. A recursive rule assigns node support levels while bounding how many hyperedges each member can represent. For a candidate, matching rank measures available support, and deletion responses identify individual and joint dependencies. A compact readout combines the rank profile with degrees of the pair-response matrix. We prove that capacity levels retain information beyond pairwise projections and satisfy a sharp member-removal bound. We also characterize the deletion responses and prove that the degree branch strictly enlarges the model's function class even when all other inputs, including the rank profile, agree. Across seven datasets, CapacityDegree outperforms eight baselines in AP and AUC, improving macro AP by 9.26 percentage points over the strongest baseline.