  Graph neural networks (GNNs) are deep learning architectures for machine
learning problems on graphs. It has recently been shown that the expressiveness
of GNNs can be characterised precisely by the combinatorial Weisfeiler-Leman
algorithms and by finite variable counting logics. The correspondence has even
led to new, higher-order GNNs corresponding to the WL algorithm in higher
dimensions.
  The purpose of this paper is to explain these descriptive characterisations
of GNNs.
