In view of the huge success of convolution neural networks (CNN) for image classification and object recognition, there have been attempts to generalize the method to general graph-structured data. One major direction is based on spectral graph theory and graph signal processing. In this paper, we study the problem from a completely different perspective, by introducing parallel flow decomposition of graphs. The essential idea is to decompose a graph into families of non-intersecting one dimensional (1D) paths, after which, we may apply a 1D CNN along each family of paths. We demonstrate that the our method, which we call GraphFlow, is able to transfer CNN architectures to general graphs. To show the effectiveness of our approach, we test our method on the classical MNIST dataset, synthetic datasets on network information propagation and a news article classification dataset.
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