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Graph Convolutional Networks (GCNs) show promising results for semi-supervised learning tasks on graphs, thus become favorable comparing with other approaches. Despite the remarkable success of GCNs, it is difficult to train GCNs with insufficient supervision. When labeled data are limited, the performance of GCNs becomes unsatisfying for low-degree nodes. While some prior work analyze successes and failures of GCNs on the entire model level, profiling GCNs on individual node level is still underexplored.

In this paper, we analyze GCNs in regard to the node degree distribution. From empirical observation to theoretical proof, we confirm that GCNs are biased towards nodes with larger degrees with higher accuracy on them, even if high-degree nodes are underrepresented in most graphs. We further develop a novel Self-Supervised-Learning Degree-Specific GCN (SL-DSGCN) that mitigate the degree …