  Recently, Graph Convolutional Networks (GCNs) and their variants have been
receiving many research interests for learning graph-related tasks. While the
GCNs have been successfully applied to this problem, some caveats inherited
from classical deep learning still remain as open research topics in the
context of the node classification problem. One such inherited caveat is that
GCNs only consider the nodes that are a few propagations away from the labeled
nodes to classify them. However, taking only a few propagation steps away nodes
into account defeats the purpose of using the graph topological information in
the GCNs. To remedy this problem, the-state-of-the-art methods leverage the
network diffusion approaches, namely personalized page rank and its variants,
to fully account for the graph topology, {\em after} they use the Neural
Networks in the GCNs. However, these approaches overlook the fact that the
network diffusion methods favour high degree nodes in the graph, resulting in
the propagation of labels to unlabeled centralized, hub, nodes. To address this
biasing hub nodes problem, in this paper, we propose to utilize a
dimensionality reduction technique conjugate with personalized page rank so
that we can both take advantage from graph topology and resolve the hub node
favouring problem for GCNs. Here, our approach opens a new holistic road for
message passing phase of GCNs by suggesting the usage of other proximity
matrices instead of well-known Laplacian. Testing on two real-world networks
that are commonly used in benchmarking GCNs' performance for the node
classification context, we systematically evaluate the performance of the
proposed methodology and show that our approach outperforms existing methods
for wide ranges of parameter values with very limited deep learning training
{\em epochs}.
