  Exploiting symmetries and invariance in data is a powerful, yet not fully
exploited, way to achieve better generalisation with more efficiency. In this
paper, we introduce two graph network architectures that are equivariant to
several types of transformations affecting the node coordinates. First, we
build equivariance to any transformation in the coordinate embeddings that
preserves the distance between neighbouring nodes, allowing for equivariance to
the Euclidean group. Then, we introduce angle attributes to build equivariance
to any angle preserving transformation - thus, to the conformal group. Thanks
to their equivariance properties, the proposed models can be vastly more data
efficient with respect to classical graph architectures, intrinsically equipped
with a better inductive bias and better at generalising. We demonstrate these
capabilities on a synthetic dataset composed of $n$-dimensional geometric
objects. Additionally, we provide examples of their limitations when (the
right) symmetries are not present in the data.
