The number of interactions, or connectivity, among proteins in the yeast protein interaction network follows a power law. I compare patterns of connectivity for subsets of yeast proteins associated with senescence and with five other traits. I find that proteins associated with ageing have significantly higher connectivity than expected by chance, a pattern not seen for most other datasets. The pattern holds even when controlling for other factors also associated with connectivity, such as localization of protein expression within the cell. I suggest that these observations are consistent with the antagonistic pleiotropy theory for the evolution of senescence. In further support of this argument, I find that a protein's connectivity is positively correlated with the number of traits it influences or its degree of pleiotropy, and further show that the average degree of pleiotropy is greatest for proteins associated with senescence. I explain these results with a simple mathematical model combining assumptions of the antagonistic pleiotropy theory for the evolution of senescence with data on network topology. These findings integrate molecular and evolutionary models of senescence, and should aid in the search for new ageing genes.