From nodes to edges: Edge-centric GNNs for distribution grid reliability

Edge classification remains challenging for Graph Neural Networks (GNNs), as most standard architectures are designed primarily for node- or graph-level prediction. In many applications, however, decisions depend on identifying critical edges rather than individual nodes or entire graphs. This paper studies edge classification on graph-structured data and introduces GINEE (GIN with Evolving Edges), an edge-centric GNN that explicitly maintains and updates edge representations across message-passing layers. We focus on medium-voltage power grids as a safety-critical application domain, where edge classification corresponds to identifying cables whose outage leads to a violation of the n-1 contingency criterion. In this setting, we show that a node-centric baseline (GIN) achieves low recall on critical edges compared to edge-aware formulations. We evaluate GINEE against GIN variants with static edge embeddings and a line-graph-based formulation that enables direct edge–edge message passing. Experiments on realistic medium-voltage grid data from a Dutch DSO show that GINEE achieves the best overall recall and balanced accuracy: explicit edge features account for most of the performance gain, while evolving edge states provide a further consistent improvement. The line-graph reformulation underperforms edge-aware models on the original graph and incurs substantially higher inference cost, suggesting that explicit edge modelling without graph transformation is the more effective inductive bias for safety-critical edge classification.