The　prediction　of　river　runoff　in　a　small　or　medium-sized　catchment　is　constrained　by　the　spatial　distribution　and　density　of　its　rain　gauges　and　record　length　historical　rainfall　data.　To　enhance　the　accuracy　of　flash　flood　early　warning　and　forecasting　for　such　catchments,　this　study　redefines　the　data　structure　of　an　hourly　rainfall-runoff　model　based　on　the　graph　theory　and　the　2000-2014　data　of　the　Shaxi　River　basin.　We　use　graph　neural　networks　(GNNs)　to　construct　an　end-to-end　dynamic　mapping　model　for　its　rainfall-runoff　data,　and　predict　its　future　hydrographs　at　different　forecast　periods,　using　Graph　Convolutional　Neural　Network　(GCN),　Graph　Attention　Network　(GAT),　and　Chebyshev　Graph　Neural　Network　(Chebnet)　models.　Mean　Absolute　Error　(EMAE)　is　used　as　an　evaluation　indicator　to　compare　the　predictions　for　the　next　two　hours　with　those　by　the　Long　Short-Term　Memory　(LSTM)　models,　Gated　Recurrent　Unit　(GRU),　and　Artificial　Neural　Networks　(ANNs).　The　results　indicate　that　for　this　basin,　the　Chebnet　and　GAT　models　are　superior　in　nonlinear　data　fitting　capability　for　rainfall-runoff　predictions　at　the　forecast　periods　of　one　and　two　hours,　improving　prediction　accuracy　by　37.3%　to　64.7%　compared　to　LSTM　and　GRU.　The　Chebnet　model　exhibits　stable　performance　in　its　runoff　prediction　of　the　next　15　hours,　significantly　reducing　the　impact　of　timeliness　while　improving　accuracy　and　applicability.　This　study　has　achieved　highly　reliable　predictions　of　river　runoff,　useful　for　early　flood　warning　in　small　and　medium-sized　catchments.　©　2025　Tsinghua　University.　All　rights　reserved.