  Graph Convolutional Networks (GCNs) have achieved impressive performance in a
wide variety of areas, attracting considerable attention. The core step of GCNs
is the information-passing framework that considers all information from
neighbors to the central vertex to be equally important. Such equal importance,
however, is inadequate for scale-free networks, where hub vertices propagate
more dominant information due to vertex imbalance. In this paper, we propose a
novel centrality-based framework named CenGCN to address the inequality of
information. This framework first quantifies the similarity between hub
vertices and their neighbors by label propagation with hub vertices. Based on
this similarity and centrality indices, the framework transforms the graph by
increasing or decreasing the weights of edges connecting hub vertices and
adding self-connections to vertices. In each non-output layer of the GCN, this
framework uses a hub attention mechanism to assign new weights to connected
non-hub vertices based on their common information with hub vertices. We
present two variants CenGCN\_D and CenGCN\_E, based on degree centrality and
eigenvector centrality, respectively. We also conduct comprehensive
experiments, including vertex classification, link prediction, vertex
clustering, and network visualization. The results demonstrate that the two
variants significantly outperform state-of-the-art baselines.
