With the rapid development of the World Wide Web (WWW), heterogeneous graphs (HG) have explosive growth. Recently, heterogeneous graph neural network (HGNN) has shown great potential in learning on HG. Current studies of HGNN mainly focus on some HGs with strong homophily properties (nodes connected by meta-path tend to have the same labels), while few discussions are made in those that are less homophilous. Recently, there have been many works on homogeneous graphs with heterophily. However, due to heterogeneity, it is non-trivial to extend their approach to deal with HGs with heterophily. In this work, based on empirical observations, we propose a meta-path-induced metric to measure the homophily degree of a HG. We also find that current HGNNs may have degenerated performance when handling HGs with less homophilous properties. Thus it is essential to increase the generalization ability of HGNNs on non-homophilous HGs. To this end, we propose HDHGR, a homophily-oriented deep heterogeneous graph rewiring approach that modifies the HG structure to increase the performance of HGNN. We theoretically verify HDHGR. In addition, experiments on real-world HGs demonstrate the effectiveness of HDHGR, which brings at most more than 10% relative gain.

Graph Transformers have proved their advantages in graph data mining with elaborate Positional Encodings, especially in graph-level tasks. However, their application in the node classification task has not been fully exploited yet. In the node classification task, existing Graph Transformers with Positional Encodings are limited by the following issues: (i) PEs describing the node’s positional identities are insufficient for the node classification task on complex graphs, where a full portrayal of the local node property is needed. (ii) PEs for graphs are integrated with Transformers in a constant schema, resulting in the ignorance of local patterns that may vary among different nodes. In this paper, we propose Adaptive Graph Transformer (AGT) to tackle above issues. AGT consists of a Learnable Centrality Encoding and a Kernelized Local Structure Encoding. The two modules extract structural patterns from centrality and subgraph views in a learnable and scalable manner. Further, we design the Adaptive Transformer Block to adaptively integrate the attention scores and Structural Encodings in a node-specific manner. AGT achieves state-of-the-art performances on nine real-world web graphs (up to 1.6 million nodes). Furthermore, AGT shows outstanding results on two series of synthetic graphs with ranges of heterophily and noise ratios.