  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.
