Title: FlowX: Towards Explainable Graph Neural Networks via Message Flows. Abstract: We investigate the explainability of graph neural networks (GNNs) as a step towards elucidating their working mechanisms. While most current methods focus on explaining graph nodes, edges, or features, we argue that, as the inherent functional mechanism of GNNs, message flows are more natural for performing explainability. To this end, we propose a novel method here, known as FlowX, to explain GNNs by identifying important message flows. To quantify the importance of flows, we propose to employ the concept of Shapley values from cooperative game theory. To tackle the complexity of computing Shapley values, we propose an approximation scheme to compute Shapley values as initial assessments of flow importance. We then propose a learning algorithm to refine scores and improve explainability. Experimental studies on both synthetic and real-world datasets demonstrate that our proposed FlowX leads to improved explainability of GNNs.