# SR-GNN: A Signed Network Embedding Method Guided by Status Theory and a Reciprocity Relationship
## 2 Related Work  
In this section, we review related works. First, we simply review GNN for unsigned networks. Then, we review GNN for undirected signed networks based on the (weak) balance theory. Finally, we review directed signed network representation learning methods. In recent years, deep learning models represented by Graph Neural Networks (GNNs) have garnered significant attention from specialists across numerous domains due to their remarkable performance and have become an important tool and method for graph representation learning. Most GNN models are developed based on the Message-Passing Neural Network (MPNN) [10; 11] technique, which \"aggregates neighbor information and updates the node's own state\" by creating information passing, aggregation, and optimization algorithms. This technique turns the rich structure and semantic information of the graph into low-dimensional vector representations of nodes. Based on these vector representations, numerous downstream tasks on unsigned networks are implemented, achieving good results in node classification [12], link prediction [13], and graph clustering [14]. It is feasible and necessary to do research on signed networks utilizing GNNs. However, applying the MPNN paradigm for signed network representation learning faces considerable challenges: GNNs were originally designed for analyzing undirected graphs without heterogeneous edge properties, making it difficult to handle the heterogeneity and directed edges in graphs. To enable GNNs to analyze the positive/negative features, various scientists have made efforts: [PERSON] et al. [4] integrated structural balance theory with standard graph convolution in introducing SGCN, the first signed neural network model. Subsequently, researchers incorporated attention mechanisms [5], graph contrastive learning [15], mutual information [16], and random walks [17; 18] into the study of signed networks. Recent work [6] proposed a new network model that combines the global community structure brought by (weak) structural balance. This model consists of global and local GNN structures. In the global module, a more generalized k-balanced network is used to learn node representations; the local module employs a relation GNN without prior assumptions to complement the global module. The above research is based on (weak) structural balance theory, establishing optimization objectives for GNN models to \"bring closer\" nodes connected by positive edges and \"push away\" nodes connected by negative edges. Such embedding representations can be employed for downstream tasks like node classification and sign prediction but are not suited for node ranking tasks. Models based on (weak) structural balance theory can only handle undirected signed networks. Researchers suggest that the direction of edges is crucial to the structure of networks. Fully utilizing this feature may enhance the forecasting capability of GNN models [19]. To leverage the directionality of edges in signed networks, a few researchers proposed the following models: SDGNN [20], S-GNN [21], BESIDE [22], and SIDE [18], among which SDGNN and S-GNN are deep models, and BESIDE and SIDE are shallow network embedding. SDGNN attempts to use motifs to define edges in different directions and the triangular structural features formed by these edges, obtaining a more accurate node vector representation. Nevertheless, the introduction of higher-order features unavoidably entails more computational complexity, so an improved methodology is essential to exploit edge direction. S-GNN uses state theory to define the aggregation methods for positive and negative edges in the sending and receiving of directions, respectively.