A Spectral Gap-Guided Eulerian Graph Rewiring Method for Heterogeneous Graph Embedding.

Structure-based graph rewiring, a graph augmentation approach, modifies the graph structure for enhancing the graph connectivity while keeping the graph intrinsic semantics, improving node embeddings in heterogeneous graphs. To augment the graph connectivity while avoiding introducing more noise into the graph, this paper proposes a novel model EulerRewire for heterogeneous graph by identifying all pairs of nodes with odd degree and adding edges between these node pairs while the graph spectral gap is utilized to guide edge selection, adding edges as few and enhancing the graph connectivity as much as possible. Then, a dual-view encoder based on GCN and Transformer to jointly learn node embeddings in the rewired Eulerian graph due to their abilities in capturing local structure and high-order dependency, in which a circuit sequence is generated for each node in the rewired Eulerian graph, better capturing high-order dependency between nodes. Extensive experiments for three downstream tasks including node classification, node clustering and link prediction demonstrate the proposed EulerRewire is superior to state-of-the-art baselines in most datasets.