The message-passing mechanism of graph convolutional networks (i.e., GCNs) enables label information to reach more unlabeled neighbors, thereby increasing the utilization of labels. However, the additional label information does not always contribute positively to the GCN. To address this issue, we propose a new two-step framework called ELU-GCN. In the first stage, ELU-GCN conducts graph learning to learn a new graph structure (i.e., ELU-graph), which allows the additional label information to positively influence the predictions of GCN. In the second stage, we design a new graph contrastive learning on the GCN framework for representation learning by exploring the consistency and mutually exclusive information between the learned ELU graph and the original graph. Moreover, we theoretically demonstrate that the proposed method can ensure the generalization ability of GCNs. Extensive experiments validate the superiority of our method.

Despite their excellent performance in graph representation learning, graph convolutional networks have been proved to be vulnerable to adversarial perturbations on the connectivity between nodes in an unnoticed manner. In this work, by looking into the impacts of adversarial attacks on graph data, we empirically find that the dominant edge-addition attacks generally increase the heterophily between connected nodes, which will fool the transductive inference models on node classification task. To defend against such attacks, we develop a Two-Stage Denoising (TSD) method that aims at removing possible malicious edges so as to mitigate the heterophily issue introduced by attacks. In particular, after a rough removal of the links that have quite low feature similarity, our method further spots the potentially heterophilous links by predicting node labels with a multi-view labeling consensus. This design is based on assumption that if the label predictions for the same node from two different views of a graph data are consistent, then we have a high chance to acquire the reliable labeling. The experiments demonstrate that by denoising a graph this way, the robustness of graph convolutional networks on node classification task is remarkably improved, compared to several strong competitive robust graph neural network models.

The label smoothness assumption is at the core of Graph Convolutional Networks (GCNs): nodes in a local region have similar labels. Thus, GCN performs local feature smoothing operation to adhere to this assumption. However, there exist some nodes whose labels obtained by feature smoothing conflict with the label smoothness assumption. We find that the label smoothness assumption and the process of feature smoothing are both problematic on these nodes, and call these nodes out of GCN's control (OOC nodes). In this paper, first, we design the corresponding algorithm to locate the OOC nodes, then we summarize the characteristics of OOC nodes that affect their representation learning, and based on their characteristics, we present DaGCN, an efficient framework that can facilitate the OOC nodes. Extensive experiments verify the superiority of the proposed method and demonstrate that current advanced GCNs are improvements specifically on OOC nodes; the remaining nodes under GCN's control (UC nodes) are already optimally represented by vanilla GCN on most datasets.

Graph representation learning aims at integrating node contents with graph structure to learn nodes/graph representations. Nevertheless, it is found that many existing graph learning methods do not work well on data with high heterophily level that accounts for a large proportion of edges between different class labels. Recent efforts to this problem focus on improving the message passing mechanism. However, it remains unclear whether heterophily truly does harm to the performance of graph neural networks (GNNs). The key is to unfold the relationship between a node and its immediate neighbors, e.g., are they heterophilous or homophilious? From this perspective, here we study the role of heterophily in graph representation learning before/after the relationships between connected nodes are disclosed. In particular, we propose an end-to-end framework that both learns the type of edges (i.e., heterophilous/homophilious) and leverage edge type information to improve the expressiveness of graph neural networks. We implement this framework in two different ways. Specifically, to avoid messages passing through heterophilous edges, we can optimize the graph structure to be homophilious by dropping heterophilous edges identified by an edge classifier. Alternatively, it is possible to exploit the information about the presence of heterophilous neighbors for feature learning, so a hybrid message passing approach is devised to aggregate homophilious neighbors and diversify heterophilous neighbors based on edge classification. Extensive experiments demonstrate the remarkable performance improvement of GNNs with the proposed framework on multiple datasets across the full spectrum of homophily level.

Multiple recent studies show a paradox in graph convolutional networks (GCNs)—that is, shallow architectures limit the capability of learning information from high-order neighbors, whereas deep architectures suffer from over-smoothing or over-squashing. To enjoy the simplicity of shallow architectures and overcome their limits of neighborhood extension, in this work we introduce a biaffine technique to improve the expressiveness of GCNs with a shallow architecture. The core design of our method is to learn direct dependency on long-distance neighbors for nodes, with which only 1-hop message passing is capable of capturing rich information for node representation. Besides, we propose a multi-view contrastive learning method to exploit the representations learned from long-distance dependencies. Extensive experiments on nine graph benchmark datasets suggest that the shallow biaffine graph convolutional networks (BAGCN) significantly outperform state-of-the-art GCNs (with deep or shallow architectures) on semi-supervised node classification. We further verify the effectiveness of biaffine design in node representation learning and the performance consistency on different sizes of training data.

Graph convolutional networks (GCNs) are currently the most promising paradigm for dealing with graph-structure data, while recent studies have also shown that GCNs are vulnerable to adversarial attacks. Thus developing GCN models that are robust to such attacks become a hot research topic. However, the structural purification learning-based or robustness constraints-based defense GCN methods are usually designed for specific data or attacks, and introduce additional objective that is not for classification. Extra training overhead is also required in their design. To address these challenges, we conduct in-depth explorations on mid-frequency signals on graphs and propose a simple yet effective Mid-pass filter GCN (Mid-GCN). Theoretical analyses guarantee the robustness of signals through the mid-pass filter, and we also shed light on the properties of different frequency signals under adversarial attacks. Extensive experiments on six benchmark graph data further verify the effectiveness of our designed Mid-GCN in node classification accuracy compared to state-of-the-art GCNs under various adversarial attack strategies.

In graph learning, it is fundamental to integrate the features from graph structure and node attributes. Towards this end, graph convolution technique has been devised based on the premise that the similarity of node attributes between two nodes is semantically consistent with their topological proximity. However, many real-networks are found to exhibit the semantic inconsistency, i.e., the phenomenon that directly connected nodes are dissimilar in their attributes. This work is concerned with two related issues: how do we quantitatively measure the semantic consistency between node attributes and graph structure? can we leverage this information to facilitate graph representation? To answer those questions, we first introduce a novel metric to evaluate the semantic consistency in a graph, and then we identify a set of key designs to encode the local semantic consistency information into a type of ego's node feature. Then, we fuse this new node feature with the original node attributes by concatenating the two parts using the semantic consistency metric as weight factor. Experiments on real-world datasets show that linear classifier (e.g. multilayer perceptrons) based on our unsupervised feature learning scheme achieves strong performance across the datasets, especially on the datasets with low semantic consistency, compared to the popular supervised GCNs and other competitive unsupervised graph representation learning models.