<![CDATA[Soil nutrient prediction is a spatial modeling problem because nutrient values observed at nearby locations may share common spatial structure. This study develops a graph-theoretic analysis of weighted neighborhood graphs for Graph Convolutional Network (GCN)-based prediction of synthetic nitrogen (N), phosphorus (P), and potassium (K) patterns. Ten independent Monte Carlo realizations of 100 sampling locations were generated from a uniform distribution on the unit square. For each realization, weighted k-nearest-neighbor (kNN) and epsilon-neighborhood graphs were constructed using an exponential distance-decay kernel. Graph structure was quantified using the number of edges, average degree, density, number of connected components, and algebraic connectivity. Separate transductive GCN regressors were trained for N, P, and K using train-validation-test splits, target standardization based only on the training set, early stopping, and repeated random seeds. Binary GCN, multilayer perceptron (MLP), Random Forest, and inverse-distance weighting (IDW) were included as baselines. Among the tested graph configurations, kNN with gave the lowest mean test error , whereas kNN with produced a marginally higher mean . Weighted GCN improved numerically over binary GCN overall , with a significant paired improvement in MAE under a Wilcoxon test , although MLP remained slightly stronger overall . Across graph configurations, density was negatively associated with test indicating that excessive neighborhood mixing can reduce predictive performance in these controlled settings. Nutrient-specific analysis showed that phosphorus was the most difficult target, while residual Moran’s I values were close to zero. Within the controlled synthetic scenarios, weighted neighborhood graphs provided a useful and interpretable representation for GCN-based spatial nutrient modeling. Future work should evaluate the framework on field measurements using spatial block validation and environmental covariates.]]>
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