  Cellular function is widely believed to be organized in a modular fashion. On
all scales and at all levels of complexity, relatively independent sub-units
perform relatively independent sub-tasks of biological function. This
functional modularity must be reflected in the topology of molecular networks.
But how a functional module should be represented in an interaction network is
an open question. In protein-interaction networks (PIN), one can identify a
protein-complex as a module on a small scale, i.e. modules are understood as
densely linked, resp. interacting, groups of proteins, that are only sparsely
interacting with the rest of the network.
  In this contribution, we show that extrapolating this concept of cohesively
linked clusters of proteins as modules to the scale of the entire PIN
inevitable misses important and functionally relevant structure inherent in the
network. As an alternative, we introduce a novel way of decomposing a network
into functional roles and show that this represents network structure and
function more efficiently. This finding should have a profound impact on all
module assisted methods of protein function prediction and should shed new
light on how functional modules can be represented in molecular interaction
networks in general.
