Irregular data in the real world are usually organized as heterogeneous graphs consisting of multiple types of nodes and edges. However, current heterogeneous graph research confronts three fundamental challenges: i) Benchmark Deficiency, ii) Semantic Disalignment, and iii) Propagation Degradation. In this paper, we construct a large-scale, universal, and joint multi-domain heterogeneous graph dataset named UniHG to facilitate heterogeneous graph representation learning and cross-domain knowledge mining. Overall, UniHG contains 77.31 million nodes and 564 million directed edges with thousands of labels and attributes, which is currently the largest universal heterogeneous graph dataset available to the best of our knowledge. To perform effective learning and provide comprehensively benchmarks on UniHG, two key measures are taken, including i) the semantic alignment strategy for multi-attribute entities, which projects the feature description of multi-attribute nodes and edges into a common embedding space to facilitate information aggregation; ii) proposing the novel Heterogeneous Graph Decoupling (HGD) framework with a specifically designed Anisotropy Feature Propagation (AFP) module for learning effective multi-hop anisotropic propagation kernels. These two strategies enable efficient information propagation among a tremendous number of multi-attribute entities and meanwhile mine multi-attribute association adaptively through the multi-hop aggregation in large-scale heterogeneous graphs. Comprehensive benchmark results demonstrate that our model significantly outperforms existing methods with an accuracy improvement of 28.93%. And the UniHG can facilitate downstream tasks, achieving an NDCG@20 improvement rate of 11.48% and 11.71%.

A.1 Proof of Theorem 1 In this proof, we adopt a simplified version of our message-passing function that ignores the skipconnection: The HGNN trained in the experimental results shown in Figure 2 also does not use skip-connections and hence represents a theoretically-exact KTN component. In the real experiments, we use (1) skip-connections, exploiting their usual benefits (12), and (2) the trainable version of KTN. Without loss of generality, we prove the result for the case where R = {(s,t): s,t T }, meaning the type of an edge is identified with the (ordered) types of the neighbor nodes. In other words, there is only one edge modality possible, such as a social networks with multiple node types (e.g. "friendship" and "message"), the result is extended trivially (through with more algebraically-dense forms of ats and qts). The output of Aggregate is a concatenation of edge-type-specific aggregations (see Equation 3).

Utilizing long-range dependency, a concept extensively studied in homogeneous graphs, remains underexplored in heterogeneous graphs, especially on large ones, posing two significant challenges: Reducing computational costs while maximizing effective information utilization in the presence of heterogeneity, and overcoming the over-smoothing issue in graph neural networks. To address this gap, we investigate the importance of different meta-paths and introduce an automatic framework for utilizing long-range dependency on heterogeneous graphs, denoted as Long-range Meta-path Search through Progressive Sampling (LMSPS). Specifically, we develop a search space with all meta-paths related to the target node type. By employing a progressive sampling algorithm, LMSPS dynamically shrinks the search space with hop-independent time complexity. Through a sampling evaluation strategy, LMSPS conducts a specialized and effective meta-path selection, leading to retraining with only effective meta-paths, thus mitigating costs and over-smoothing.

Thelimitations especially become problematic when learning representations on a misspecified graph or a heterogeneous graph that consists of various types of nodes and edges.

Each distribution quantifies the descriptive degrees of various classes given a specific instance.