Convolution acts as a local feature extractor in convolutional neural networks (CNNs). However, the convolution operation is not applicable when the input data is supported on an irregular graph such as with social networks, citation networks, or knowledge graphs. This paper proposes the topology adaptive graph convolutional network (TAGCN), a novel graph convolutional network that generalizes CNN architectures to graph-structured data and provides a systematic way to design a set of fixed-size learnable filters to perform convolutions on graphs. The topologies of these filters are adaptive to the topology of the graph when they scan the graph to perform convolution, replacing the square filter for the grid-structured data in traditional CNNs. The outputs are the weighted sum of these filters’ outputs, extraction of both vertex features and strength of correlation between vertices. It
 can be used with both directed and undirected graphs. The proposed TAGCN not only inherits the properties of convolutions in CNN for grid-structured data, but it is also consistent with convolution as defined in graph signal processing. Further, as no approximation to the convolution is needed, TAGCN exhibits better performance than existing graph-convolution-approximation methods on a number
 of data sets. As only the polynomials of degree two of the adjacency matrix are used, TAGCN is also computationally simpler than other recent methods.
Low computational complexity graph CNN (without approximation) with better classification accuracy Proposes a new CNN approach to graph classification using a filter based on outgoing walks of increasing length to incorporate information from more distant vertices in one propagation step. Proposal for a new neural network architecture for semi-supervised graph classification, building upon graph polynomial filters and utilizing them on successive neural network layers with ReLU activation functions. The paper introduces Topology Adaptive GCN to generalize convolutional networks to graph-structured data