Ontologies have proven very useful for capturing knowledge as a hierarchy of terms and their interrelationships. In biology a major challenge has been to construct ontologies of gene function given incomplete biological knowledge and inconsistencies in how this knowledge is manually curated. Here we show that large networks of gene and protein interactions in Saccharomyces cerevisiae can be used to infer an ontology whose coverage and power are equivalent to those of the manually curated Gene Ontology (GO). The network-extracted ontology (NeXO) contains 4,123 biological terms and 5,766 term-term relations, capturing 58% of known cellular components. We also explore robust NeXO terms and term relations that were initially not cataloged in GO, a number of which have now been added based on our analysis. Using quantitative genetic interaction profiling and chemogenomics, we find further support for many of the uncharacterized terms identified by NeXO, including multisubunit structures related to protein trafficking or mitochondrial function. This work enables a shift from using ontologies to evaluate data to using data to construct and evaluate ontologies.