Spatio-temporal graph neural networks combine a node's history with information from graph neighbors. The central question is whether graph neighbors provide predictive information beyond each node's own history. Forecast accuracy depends on both the choice of neighbors and the way graph messages enter the temporal model. We study these choices as graph construction and graph exposure on U.S. state unemployment, traffic speed, and electricity demand. Our diagnostic design uses two comparisons: varying exposure while holding the domain graph fixed, and varying construction while holding late gated integration fixed. A GRU using only each node's own history and randomized graph controls help assess what the graph contributes. Under a common change forecasting protocol, the same domain graph can improve or worsen error relative to the GRU across integration designs. Late integration alone is insufficient, while adding a fusion gate yields lower mean error in all three tasks. With late gated integration fixed, a graph based on residual correlations has the lowest mean error among the tested graphs, although randomized graphs perform similarly on unemployment. The findings support evaluating graph construction and integration together, with conclusions tied to the comparisons actually performed.

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