The organization of a cell emerges from the interactions in protein networks. The interactome is critically dependent on the strengths of interactions and the cellular abundances of the connected proteins, both of which span orders of magnitude. However, these aspects have not yet been analyzed globally. Here, we have generated a library of HeLa cell lines expressing 1,125 GFP-tagged proteins under near-endogenous control, which we used as input for a next-generation interaction survey. Using quantitative proteomics, we detect specific interactions, estimate interaction stoichiometries, and measure cellular abundances of interacting proteins. These three quantitative dimensions reveal that the protein network is dominated by weak, substoichiometric interactions that play a pivotal role in defining network topology. The minority of stable complexes can be identified by their unique stoichiometry signature. This study provides a rich interaction dataset connecting thousands of proteins and introduces a framework for quantitative network analysis.