## 2 Related Work  
The primary objective of this article is to introduce an innovative approach to representation learning on KGs that leverages the attention mechanism of GNNs for KGC reasoning tasks. To achieve this, we conducted a literature review encompassing KG embeddings for KGC, advancements in GNN-based KGC, and models that incorporate multi-relational GNNs. Unlike traditional embedding-based and GNN-based KGC models, the Relgraph framework excels at capturing relational dependencies within GNNs, enabling more effective KG embedding learning and subsequently enhancing the performance of KGC models.  
**KGC via KG embeddings.** The utilization of learnable embeddings for KGs has spawned numerous works aimed at KGC tasks. For instance, references [6; 7; 8; 9; 10] describe methods that learn to map KG relations into vector spaces and employ scoring functions for KGC tasks. In contrast, NTN [11] parameterizes each relation using a neural network. Paper [12] proposes a divide-search-combine algorithm, RelEns-DSC, to efficiently search relation-aware ensemble weights for KG embedding. The common drawback of these methods is that they cannot explicitly model the relationships between predicates.  
**KGC via GNNs.** GNN is a framework introduced by [13] for learning deep models or embeddings on graph-structured data. The theoretical foundation for GNNs' ability to capture common graph heuristics for KGC tasks in simple graphs was established by [14]. Furthermore, ref. [15] employed a similar approach to achieve competitive results on inductive matrix completion. Homogeneous GNN models are often unable to directly apply to tasks involving multiple relations.  
**Multi-relational GNNs.** Multi-relational GNNs have been widely studied in recent years as a powerful tool for enhancing knowledge representation and reasoning on KGs [4; 5]. These networks aim to capture the complex relationships between entities and  
Figure 2: The toy kinship knowledge graph (KG) (**top**) and its corresponding relation graph (**bottom**). In the knowledge graph above, vertices represent entities, and links represent relations (or predicates) in the knowledge graph. In the relation graph, vertices represent relations from the knowledge graph, links represent entity links (red dashed line). The presence of an entity link between vertices is determined by Equation (2).  
predicates in KGs. One line of research focuses on introducing more complex network architectures to capture the multi-relational interactions better [16]. These models often involve the use of attention mechanisms or graph convolutional layers to capture the interactions between different relations explicitly. Another line of research aims to effectively develop learning algorithms that can optimize the representations learned by multi-relational GNNs [4]. Paper [17] proposes an adaptive propagation path learning method for GNN-based inductive KG reasoning, addressing the limitations of hand-designed paths and the explosive growth of entities. [PERSON] [18] leverages Triple2 Seq to handle heterogeneity and a structure-enhanced self-attention mechanism to encode relational information. These algorithms often involve the use of contrastive learning or other optimization techniques to improve the performance of representation learning and reasoning tasks on KGs. However, they often cannot explicitly model the relationships between predicates, which limits their accuracy and efficiency in conducting knowledge graph reasoning.