  Graph Convolutional Networks (GCN) are Graph Neural Networks where the
convolutions are applied over a graph. In contrast to Convolutional Neural
Networks, GCN's are designed to perform inference on graphs, where the number
of nodes can vary, and the nodes are unordered. In this study, we address two
important challenges related to GCNs: i) oversmoothing; and ii) the utilization
of node relational properties (i.e., heterophily and homophily). Oversmoothing
is the degradation of the discriminative capacity of nodes as a result of
repeated aggregations. Heterophily is the tendency for nodes of different
classes to connect, whereas homophily is the tendency of similar nodes to
connect. We propose a new strategy for addressing these challenges in GCNs
based on Transfer Entropy (TE), which measures of the amount of directed
transfer of information between two time varying nodes. Our findings indicate
that using node heterophily and degree information as a node selection
mechanism, along with feature-based TE calculations, enhances accuracy across
various GCN models. Our model can be easily modified to improve classification
accuracy of a GCN model. As a trade off, this performance boost comes with a
significant computational overhead when the TE is computed for many graph
nodes.
