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.