  Graph Neural Networks (GNNs) often perform better for high-degree nodes than
low-degree nodes on node classification tasks. This degree bias can reinforce
social marginalization by, e.g., sidelining authors of lowly-cited papers when
predicting paper topics in citation networks. While researchers have proposed
numerous hypotheses for why GNN degree bias occurs, we find via a survey of 38
degree bias papers that these hypotheses are often not rigorously validated,
and can even be contradictory. Thus, we provide an analysis of the origins of
degree bias in message-passing GNNs with different graph filters. We prove that
high-degree test nodes tend to have a lower probability of misclassification
regardless of how GNNs are trained. Moreover, we show that degree bias arises
from a variety of factors that are associated with a node's degree (e.g.,
homophily of neighbors, diversity of neighbors). Furthermore, we show that
during training, some GNNs may adjust their loss on low-degree nodes more
slowly than on high-degree nodes; however, with sufficiently many epochs of
training, message-passing GNNs can achieve their maximum possible training
accuracy, which is not significantly limited by their expressive power.
Throughout our analysis, we connect our findings to previously-proposed
hypotheses for the origins of degree bias, supporting and unifying some while
drawing doubt to others. We validate our theoretical findings on 8 common
real-world networks, and based on our theoretical and empirical insights,
describe a roadmap to alleviate degree bias.
