Numerous studies have suggested that hub proteins in the S. cerevisiae physical interaction network are more likely to be essential than other proteins. The proposed reasons underlying this observed relationship between topology and functioning have been subject to some controversy, with recent work suggesting that it arises due to the participation of hub proteins in essential complexes and processes. However, do these essential modules themselves have distinct network characteristics, and how do their essential proteins differ in their topological properties from their non-essential proteins? We aimed to advance our understanding of protein essentiality by analyzing proteins, complexes and processes within their broader functional context and by considering physical interactions both within and across complexes and biological processes. In agreement with the view that essentiality is a modular property, we found that the number of intracomplex or intraprocess interactions that a protein has is a better indicator of its essentiality than its overall number of interactions. Moreover, we found that within an essential complex, its essential proteins have on average more interactions, especially intracomplex interactions, than its non-essential proteins. Finally, we built a module-level interaction network and found that essential complexes and processes tend to have higher interaction degrees in this network than non-essential complexes and processes, that is, they exhibit a larger amount of functional cross-talk than their non-essential counterparts.