Why the non-exploitation of edge labels in current graph convolutions "results in an overly homogeneous view of local graph neighborhoods"? I am currently reading a paper called Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs (2017, CPPR), and I cannot understand the following sentence:

We identify that the current formulations of graph convolution do not
exploit edge labels, which results in an overly homogeneous view of
local graph neighborhoods, with an effect similar to enforcing
rotational invariance of filters in regular convolutions on images.

What does this sentence mean?
Consider a two-dimensional convolution layer with 3x3 kernels. The 2d inputs of this layer can be seen as a particular graph with each pixel being a graph node, that is connected to 8 of his neighbors:

The 3x3 kernels of the convolutional layer not only process the information about neighborhood relation between pixels, but also about their relative orientation. For example the [0,0] element of the kernel might represent the weight of the node to NW. And the [1,2] element of the kernel represent the weight the node across the S edge:

Now, if we make a convolution that &quot;doesn't exploit edge labels&quot; then we'll have to forget the labels on the picture above, making us loose directional information:

All we can say now is that the &quot;red&quot; node has those neighbors, but we don't really know how they are oriented relative to it. Since now the sub-graph does not provide any directional information, the learned convolution kernels will be direction-agnostic - in other words, they will be rotation-invariant.