Title: SoGCN: Second-Order Graph Convolutional Networks. Abstract: We introduce a second-order graph convolution (SoGC), a maximally localized kernel, that can express a polynomial spectral filter with arbitrary coefficients.  We contrast our SoGC with vanilla GCN, first-order (one-hop) aggregation, and higher-order (multi-hop) aggregation by analyzing graph convolutional layers via generalized filter space.  We argue that SoGC is a simple design capable of forming the basic building block of graph convolution, playing the same role as $3 \times 3$ kernels in CNNs.   We build purely topological Second-Order Graph Convolutional Networks (SoGCN) and demonstrate that SoGCN consistently achieves state-of-the-art performance on the latest benchmark. Moreover, we introduce the Gated Recurrent Unit (GRU) to spectral GCNs. This explorative attempt further improves our experimental results.