  Graph neural networks (GNNs) have gained traction over the past few years for
their superior performance in numerous machine learning tasks. Graph
Convolutional Neural Networks (GCN) are a common variant of GNNs that are known
to have high performance in semi-supervised node classification (SSNC), and
work well under the assumption of homophily. Recent literature has highlighted
that GCNs can achieve strong performance on heterophilous graphs under certain
"special conditions". These arguments motivate us to understand why, and how,
GCNs learn to perform SSNC. We find a positive correlation between similarity
of latent node embeddings of nodes within a class and the performance of a GCN.
Our investigation on underlying graph structures of a dataset finds that a
GCN's SSNC performance is significantly influenced by the consistency and
uniqueness in neighborhood structure of nodes within a class.
