We are faced with a flood of molecular and clinical data. We are measuring interactions between various bio-molecules in and around a cell that form large, complex systems. Patient omics datasets are also increasingly becoming available. These systems-level network data provide heterogeneous, but complementary information about cells, tissues and diseases. The challenge is how to mine them collectively to answer fundamental biological and medical questions. This is nontrivial, because of computational intractability of many underlying problems on networks (also called graphs), necessitating the development of approximate algorithms (heuristic methods) for finding approximate solutions. We develop artificial intelligence (AI) methods for extracting new biomedical knowledge from the wiring patterns of systems-level, heterogeneous omics data. Our graphlet-based and other methods uncover the patterns in molecular (omics) networks and in the multi-scale organization of these networks indicative of biological function, translating the information hidden in the network topology into domain-specific knowledge. Also, we introduce a versatile data fusion (integration) machine learning (ML) framework to address key challenges in precision medicine from the wiring patterns of omics network data: better stratification of patients, prediction of cancer related genes, and re-purposing of approved drugs to particular patients and patient groups, including Covid-19 patients. Our new methods stem from novel network science algorithms coupled with graph-regularized non-negative matrix tri-factorization (NMTF), a machine learning technique for dimensionality reduction, inference and co-clustering of heterogeneous datasets. We utilize our new framework to develop methodologies for performing other related tasks, including disease re-classification from modern, heterogeneous molecular omic data, inferring new Gene Ontology relationships, aligning multiple molecular networks, and uncovering new cancer mechanisms. Also, we utilize it to develop methodologies for understanding the molecular organization of the omics data embedding space.