Protein disorder has been frequently associated with protein-protein interaction. However, our knowledge of how protein disorder evolves within a network is limited. It is expected that physically interacting proteins evolve in a coordinated manner. This has so far been shown in their evolutionary rate, and in their gene expression levels. Here we examine the percentage of predicted disorder residues within binary and complex interacting proteins (physical and functional interactions respectively) to investigate how the disorder of a protein relates to that of its interacting partners. We show that the level of disorder of interacting proteins are correlated, with a greater correlation seen among proteins that are co-members of the same complex, and a lesser correlation between proteins that are documented as binary interactors of each other. There is a striking variation among complexes not only in their disorder, but in the extent to which the proteins within the complex differ in their levels of disorder, with RNA processes and protein binding complexes showing more variation in the disorder of their proteins, whilst other complexes show very little variation in the overall disorder of their constituent proteins. There is likely to be a stronger selection for complex subunits to have similar disorder, than is seen for proteins involved in binary interactions. Thus, binary interactions may be more resilient to changes in disorder than are complex interactions. These results add a new dimension to the role of disorder in protein networks, and highlight the potential importance of maintaining similar disorder in the members of a complex.