  Graph Convolutional Network (GCN) has shown remarkable potential of exploring
graph representation. However, the GCN aggregating mechanism fails to
generalize to networks with heterophily where most nodes have neighbors from
different classes, which commonly exists in real-world networks. In order to
make the propagation and aggregation mechanism of GCN suitable for both
homophily and heterophily (or even their mixture), we introduce block modeling
into the framework of GCN so that it can realize "block-guided classified
aggregation", and automatically learn the corresponding aggregation rules for
neighbors of different classes. By incorporating block modeling into the
aggregation process, GCN is able to aggregate information from homophilic and
heterophilic neighbors discriminately according to their homophily degree. We
compared our algorithm with state-of-art methods which deal with the
heterophily problem. Empirical results demonstrate the superiority of our new
approach over existing methods in heterophilic datasets while maintaining a
competitive performance in homophilic datasets.
