A large-scale knowledge graph enhances reproducibility in biomedical data discovery by providing a standardized, integrated framework that ensures consistent interpretation across diverse datasets. It improves generalizability by connecting data from various sources, enabling broader applicability of findings across different populations and conditions. Generating reliable knowledge graph, leveraging multi-source information from existing literature, however, is challenging especially with a large number of node sizes and heterogeneous relations. In this paper, we propose a general theoretically guaranteed statistical framework, called RENKI, to enable simultaneous learning of multiple relation types. RENKI generalizes various network models widely used in statistics and computer science. The proposed framework incorporates representation learning output into initial entity embedding of a neural network that approximates the score function for the knowledge graph and continuously trains the model to fit observed facts. We prove nonasymptotic bounds for in-sample and out-of-sample weighted MSEs in relation to the pseudo-dimension of the knowledge graph function class. Additionally, we provide pseudo-dimensions for score functions based on multilayer neural networks with ReLU activation function, in the scenarios when the embedding parameters either fixed or trainable. Finally, we complement our theoretical results with numerical studies and apply the method to learn a comprehensive medical knowledge graph combining a pretrained language model representation with knowledge graph links observed in several medical ontologies. The experiments justify our theoretical findings and demonstrate the effect of weighting in the presence of heterogeneous relations and the benefit of incorporating representation learning in nonparametric models.