## 1 Introduction  
In the field of Artificial Intelligence, knowledge graph (KG) reasoning has become a pivotal research topic. As a powerful representation, KG integrates billions of available relational facts. Its importance lies in its potential to enhance the representation and inference of knowledge, enabling more intelligent decision making and problem solving. KG is now utilized in various downstream applications, including recommendation systems [1], query answering [2], and drug discovery [3]. However, due to constraints in human knowledge and text extraction technology, even the largest KGs remain incomplete. Given that the construction of knowledge graphs involves extensive data and complex semantic relationships, there are inevitable omissions and defects. To address these issues, knowledge graph reasoning techniques fill in the gaps and optimize the knowledge graph, with a typical task being knowledge graph completion (KGC). Currently, KG reasoning has become an important research field, attracting the attention and exploration of numerous researchers. With the continuous advancement of technology and increasing application demands, KG reasoning will play a more significant role in future intelligent applications. Multi-relational graph neural networks (GNNs) [4; 5] extend traditional GNNs by considering multiple relations in the graph as distinct node attributes. This extension enables the model to capture a broader range of semantic information and better encode the contextual relationships between entities. By incorporating multiple relations, multi-relational GNNs are able to handle more complex reasoning tasks, such as transitive reasoning, role reversal, and collective entity recognition. This increased expressivity significantly improves the accuracy and scalability of knowledge graph reasoning. Despite their advantages, current multi-relational GNNs face limitations. Firstly, most existing models assume that different relations have independent impacts on entities, ignoring potential interactions between different relations. This limitation can lead to incomplete or inaccurate reasoning results. Secondly, existing models often treat all relations equally, disregarding their different levels of importance in different reasoning tasks. This uniform treatment may result in information loss or overfitting in complex reasoning tasks. Figure 1 offers an example of the interactions between predicates. In this paper, we aim to address the limitations of ignoring interactive effects between relations in existing multi-relational GNNs. We introduce the Relgraph, a novel knowledge graph reasoning framework that explores logical relationships between relations by introducing a _relation graph_. This relation graph serves as a dual graph of the original KG, treating relations of the original KG (or predicates) as entities and entities in the original KG as relations. The Relgraph explicitly models the interaction between different relations as relations on the relation graph (referred to as _entity-links_), enabling more comprehensive and accurate reasoning (corresponding to it, the relations in the original KG are actually _relation-links_). By assigning different weights to different entity links based on their importance in specific reasoning tasks, Relgraph effectively handles complex reasoning tasks while reducing information loss and overfitting. A typical original knowledge graph and its corresponding relation graph are shown in Figure 2.  
We extend the traditional graph attention network (GAT) to its dual neural network, the relation graph attention network (RGAT), and design a machine learning algorithm based on the attention mechanism to synchronously optimize the two networks. As a result, we successfully apply the Relgraph framework to knowledge graph reasoning tasks. The Relgraph framework can embed various algorithms for representation learning, such as TransE and RotateE, to optimize the representation learning of entities and relations, ultimately enhancing the reasoning performance on KGs.