# 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?

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: