Convolutional Graph Neural Networks (ConvGNNs) are designed either in the spectral domain or in the spatial domain. In this paper, we provide a theoretical framework to analyze these neural networks, by deriving some equivalence of the graph convolution processes, regardless if they are designed in the spatial or the spectral domain. We demonstrate the relevance of the proposed framework by providing a spectral analysis of the most popular ConvGNNs (ChebNet, CayleyNet, GCN and Graph Attention Networks), which allows to explain their performance and shows their limits.

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