  Scattering transforms are non-trainable deep convolutional architectures that
exploit the multi-scale resolution of a wavelet filter bank to obtain an
appropriate representation of data. More importantly, they are proven invariant
to translations, and stable to perturbations that are close to translations.
This stability property dons the scattering transform with a robustness to
small changes in the metric domain of the data. When considering network data,
regular convolutions do not hold since the data domain presents an irregular
structure given by the network topology.
  In this work, we extend scattering transforms to network data by using
multiresolution graph wavelets, whose computation can be obtained by means of
graph convolutions. Furthermore, we prove that the resulting graph scattering
transforms are stable to metric perturbations of the underlying network. This
renders graph scattering transforms robust to changes on the network topology,
making it particularly useful for cases of transfer learning, topology
estimation or time-varying graphs.
