Title: Demystifying Graph Neural Network Via Graph Filter Assessment. Abstract: Graph Neural Networks (GNNs) have received tremendous attention recently due to their power in handling graph data for different downstream tasks across different application domains. The key of GNN is its graph convolutional filters, and recently various kinds of filters are designed. However, there still lacks in-depth analysis on (1) Whether there exists a best filter that can perform best on all graph data; (2) Which graph properties will influence the optimal choice of graph filter; (3) How to design appropriate filter adaptive to the graph data. In this paper, we focus on addressing the above three questions. We first propose a novel assessment tool to evaluate the effectiveness of graph convolutional filters for a given graph. Using the assessment tool, we find out that there is no single filter as a `silver bullet' that perform the best on all possible graphs. In addition, different graph structure properties will influence the optimal graph convolutional filter's design choice. Based on these findings, we develop Adaptive Filter Graph Neural Network (AFGNN), a simple but powerful model that can adaptively learn task-specific filter. For a given graph, it leverages graph filter assessment as regularization and learns to combine from a set of base filters. Experiments on both synthetic and real-world benchmark datasets demonstrate that our proposed model can indeed learn an appropriate filter and perform well on graph tasks.