Abstract: Graph Convolutional Network (GCN) has been widely used in recommendation systems due to its unique advantages in processing graph data. It propagates node attribute information by exploiting the dependencies between nodes in the graph, which greatly improves the accuracy of node representation and thus improves recommendation performance. However, existing GCN-based recommendation methods still have difficulty in modeling deeper layers due to the over-smoothing problem, which limits the representation of higher-order relationships between users and items. To this end, we propose a novel link prediction method driven by high-order relations among items in complete graph(short for LinkCG). The LinkCG method utilizes a heterogeneous graph consisting of a user-item interaction graph and a global graph representing implicit item associations to predict user-item links. By directly modeling item associations based on user interactions, it captures higher-order relationships and mitigates the issue of data sparsity. In addition, unlike node embedding-based methods, LinkCG improves the training process and enhances recommendation accuracy by assigning link weights that represent the degree of item association. Experimental results on three publicly available datasets show that the LinkCG method, as a non-deep learning model containing only two hyperparameters, provides better performance compared to the deep learning-based baseline method. The application to social relationship data further demonstrates LinkCG can capture rich enough information about user preferences from their historical interaction items.