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This paper introduces the Spatio-Temporal Apiary Graph Convolutional Network (STAG-CN), a graph neural network that models inter-hive relationships for disease onset prediction. STAG-CN operates on a dual adjacency graph combining physical co-location and climatic sensor correlation among hive sessions, and processes multivariate IoT sensor streams through a temporal--spatial--temporal sandwich architecture built on causal dilated convolutions and Chebyshev spectral graph convolutions. Evaluated on the Korean AI Hub apiculture dataset (dataset \\#71488) with expanding-window temporal cross-validation, STAG-CN achieves an F1 score of 0.607 at a three-day forecast horizon. 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