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Graph Neural Networks (GNNs) have shown satisfying performance in various graph analytical problems. Hence, they have become the \emph{de facto} solution in a variety of decision-making scenarios. However, GNNs could yield biased results against certain demographic subgroups. Some recent works have empirically shown that the biased structure of the input network is a significant source of bias for GNNs. Nevertheless, no studies have systematically scrutinized which part of the input network structure leads to biased predictions for any given node. The low transparency on how the structure of the input network influences the bias in GNN outcome largely limits the safe adoption of GNNs in various decision-critical scenarios. In this paper, we study a novel research problem of structural explanation of bias in GNNs. Specifically, we propose a novel post-hoc explanation framework to identify two edge sets that can maximally account for the exhibited bias and maximally contribute to the fairness level of the GNN prediction for any given node, respectively. Such explanations not only provide a comprehensive understanding of bias/fairness of GNN predictions but also have practical significance in building an effective yet fair GNN model. Extensive experiments on real-world datasets validate the effectiveness of the proposed framework towards delivering effective structural explanations for the bias of GNNs. Open-source code can be found at https://github.com/yushundong/REFEREE.