Mechanisms for generating GNN explanations are crucial for building trust and mitigating biases in Graph Neural Networks (GNNs), especially in high-stakes scenarios. Most current methods optimize only for fidelity under the sparsity constraint. However, this discounts the need for interpretable explanations (those that consist of familiar motif patterns) and stable explanations (those that remain unchanged under structural perturbations). We propose a novel approach that optimizes GNN explanations across these metrics, exposing their relative weighing as a control. Experiments on various real-world datasets, including MUTAG, BA-2Motif, BAMultiShapes, and PROTEINS, suggest that our method produces higher-fidelity explanations than a state-of-the-art baseline on MUTAG and PROTEINS across all evaluated budgets, and on BA-2Motif at larger budgets, while being faster in the regime of small explanation budgets. They also indicate that our method produces more stable explanations for the MUTAG and BA-2Motif datasets. We also examine the relationship among different metrics via their induced trade-off surface and explore its dependence on the nature of the motif library.
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