Research in model organisms relies on unspoken assumptions about the conservation of protein-protein interactions across species, yet several analyses suggest such conservation is limited. Fortunately, for many purposes the crucial issue is not global conservation of interactions, but preferential conservation of functionally important ones. An observed bias towards essentiality in highly-connected proteins implies the functional importance of such "hubs". We therefore define the notion of degree-conservation and demonstrate that hubs are preferentially degree-conserved. We show that a protein is more likely to be a hub if it has a high-degree ortholog, and that once a protein becomes a hub, it tends to remain so. We also identify a positive correlation between the average degree of a protein and the conservation of its interaction partners, and we find that the conservation of individual hub interactions is surprisingly high. Our work has important implications for prediction of protein function, computational inference of PPIs, and interpretation of data from model organisms.