  Graph convolutions have gained popularity due to their ability to efficiently
operate on data with an irregular geometric structure. However, graph
convolutions cause over-smoothing, which refers to representations becoming
more similar with increased depth. However, many different definitions and
intuitions currently coexist, leading to research efforts focusing on
incompatible directions. This paper attempts to align these directions by
showing that over-smoothing is merely a special case of power iteration. This
greatly simplifies the existing theory on over-smoothing, making it more
accessible. Based on the theory, we provide a novel comprehensive definition of
rank collapse as a generalized form of over-smoothing and introduce the
rank-one distance as a corresponding metric. Our empirical evaluation of 14
commonly used methods shows that more models than were previously known suffer
from this issue.
