  The convolution operator at the core of many modern neural architectures can
effectively be seen as performing a dot product between an input matrix and a
filter. While this is readily applicable to data such as images, which can be
represented as regular grids in the Euclidean space, extending the convolution
operator to work on graphs proves more challenging, due to their irregular
structure. In this paper, we propose to use graph kernels, i.e. kernel
functions that compute an inner product on graphs, to extend the standard
convolution operator to the graph domain. This allows us to define an entirely
structural model that does not require computing the embedding of the input
graph. Our architecture allows to plug-in any type of graph kernels and has the
added benefit of providing some interpretability in terms of the structural
masks that are learned during the training process, similarly to what happens
for convolutional masks in traditional convolutional neural networks. We
perform an extensive ablation study to investigate the model hyper-parameters'
impact and show that our model achieves competitive performance on standard
graph classification and regression datasets.
