# What are the exact meaning of "lower-order structure" and "higher-order structure" in this paper?

I recently read a paper on community detection in networks. In the paper EdMot: An Edge Enhancement Approach for Motif-aware Community Detection, the authors consider the "lower-order structure" of the network at the level of individual nodes and edges. And they mentioning about some "higher-order structure" method. The point is, what is the exact meaning (definition) of lower- and higher-order structure in a network?

An example would be images of faces. The low level information might be the raw $$x, y, z$$ values of the pixels: their position and colour value. Some high level information might be the direction the face in the images is facing, from what direction the lighting in the image is coming etc.