  Graph structural information such as topologies or connectivities provides
valuable guidance for graph convolutional networks (GCNs) to learn nodes'
representations. Existing GCN models that capture nodes' structural information
weight in- and out-neighbors equally or differentiate in- and out-neighbors
globally without considering nodes' local topologies. We observe that in- and
out-neighbors contribute differently for nodes with different local topologies.
To explore the directional structural information for different nodes, we
propose a GCN model with weighted structural features, named WGCN. WGCN first
captures nodes' structural fingerprints via a direction and degree aware Random
Walk with Restart algorithm, where the walk is guided by both edge direction
and nodes' in- and out-degrees. Then, the interactions between nodes'
structural fingerprints are used as the weighted node structural features. To
further capture nodes' high-order dependencies and graph geometry, WGCN embeds
graphs into a latent space to obtain nodes' latent neighbors and geometrical
relationships. Based on nodes' geometrical relationships in the latent space,
WGCN differentiates latent, in-, and out-neighbors with an attention-based
geometrical aggregation. Experiments on transductive node classification tasks
show that WGCN outperforms the baseline models consistently by up to 17.07% in
terms of accuracy on five benchmark datasets.
