A Diagnostic Protocol for GNNs in Electricity Load Forecasting: Separating Parameter Sharing from Neighborhood Access

A graph neural network (GNN) forecasting a collection of load series combines two mechanisms, sharing parameters across series and reading neighboring series, and a gain over a non-graph model may come from either; telling them apart decides whether a graph is worth maintaining. We propose a model diagnostic protocol that compares the GNN with three reference models: a per-node network, a network shared across nodes without neighbors, and the same GNN without edges. Degree-preserving rewiring tests whether neighbor identity matters. After a tuned benchmark on regional load in France and on low-voltage feeders in the UK, we apply the protocol to deliberately short node histories, as when non-stationary demand leaves only recent observations relevant: the feeders, within one week, and a public dataset of client consumption series. On the feeders, sharing parameters recovers most of the error gap between node-specific models and GNNs, about two thirds against a regularized one. Adding the edges to an otherwise identical backbone brings a smaller gain, half or more of which disappears under rewiring. On the client series, the neighbor mean degrades the per-node model on the shorter window and the edges' gain is not consistently distinguishable from zero; on the regions of France, where each node's own history is already informative, the ranking between per-node models and GNNs changes with tuning. A synthetic study points to noisy local measurements as one regime where neighbors help. In an exploratory online aggregation, graph and non-graph forecasters appear complementary, and the weight assigned to GNNs is not proportional to their contribution. In none of the three datasets do the edges account for most of a GNN's advantage over node-specific models, so a forecasting gain should be credited to the graph only after comparison with per-node and shared references.