Network data plays a crucial role in various real-world applications, as connections between entities can be represented and analyzed through graphs. These include various types such as social, information, and technical networks. However, the complex topologies of these networks present challenges in converting graph data into machine-readable vector formats. Existing models like Graph Neural Network, Graph Attention Network, and node2vec have made strides in graph embeddings. Particularly for edge-related tasks, models like node2vec often resort to indirect methods like node concatenation for vector representation of edges, aiding in tasks like link sign prediction. In this paper, we introduce LineDi2vec, an innovative approach that uses a line graph to enhance the node2vec embedding method. This method effectively captures key social network theories, namely status and balance theories. LineDi2vec not only generalizes the original graphs, transforming the relationships between edges and nodes, but also maintains the topological integrity of the original graphs for effective node embedding by node2vec. We conducted an evaluation of LineDi2vec on four real-world datasets, focusing on link sign prediction. The results demonstrate its superior performance over traditional node concatenation methods and comparable efficacy to state-of-the-art GAT and GNN methods.