We are faced with a flood of molecular and clinical data. We are measuring interactions between various bio-molecules in a cell that form large, complex systems. Patient omics datasets are also increasingly becoming available. These systems-level 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, necessitating the development of heuristic methods for finding approximate solutions. We develop methods for extracting new biomedical knowledge from the wiring patterns of systems-level, heterogeneous, networked biomedical data. Our methods uncover the patterns in molecular networks and in the multi-scale network organization indicative of biological function, translating the information hidden in the topology into domain-specific knowledge. We introduce a versatile data fusion (integration) framework to address key challenges in precision medicine: better stratification of patients, prediction of driver genes in cancer, and re-purposing of approved drugs to particular patients and patient groups. Our new methods stem from novel network science approaches coupled with graph-regularized non-negative matrix tri-factorization, a machine learning technique for dimensionality reduction 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 level data, inferring new Gene Ontology relationships, aligning multiple molecular networks, and uncovering new cancer mechanisms.