  Graph Neural Networks (GNNs) have been a powerful tool for node
classification tasks in complex networks. However, their decision-making
processes remain a black-box to users, making it challenging to understand the
reasoning behind their predictions. Counterfactual explanations (CFE) have
shown promise in enhancing the interpretability of machine learning models.
Prior approaches to compute CFE for GNNS often are learning-based approaches
that require training additional graphs. In this paper, we propose a
semivalue-based, non-learning approach to generate CFE for node classification
tasks, eliminating the need for any additional training. Our results reveals
that computing Banzhaf values requires lower sample complexity in identifying
the counterfactual explanations compared to other popular methods such as
computing Shapley values. Our empirical evidence indicates computing Banzhaf
values can achieve up to a fourfold speed up compared to Shapley values. We
also design a thresholding method for computing Banzhaf values and show
theoretical and empirical results on its robustness in noisy environments,
making it superior to Shapley values. Furthermore, the thresholded Banzhaf
values are shown to enhance efficiency without compromising the quality (i.e.,
fidelity) in the explanations in three popular graph datasets.
